What's a solution to this problem?

Abolish the conference talk, turn everything into a giant poster session, possibly with scheduled explanations. Or use the unconference format, and everyone only talks with a table's worth of people at a time, possibly doing multiple rounds if there's interest.

Academic conferences as they work now are baaaad. No wonder people complained about them going remote for COVID, everything of value happens chatting over coffee and/or in front of posters, no one gives a shit or gains anything from the average talk, given by some tired and inexperienced PhD student who doesn't know how to communication well, thinks they have to jam their talk with overly technical language to be more impressive, and possibly has bad English to make things even harder to follow to boot. Absolute snoozefest, almost no reach outside of the very narrow group of hyper specialists already studying the same topic.

I'll answer for both sides, as the presenter and as the audience member.

As the presenter, you want to structure your talk with repetition around central points in mind, as well as rely on heuristic anchors. It's unlikely that people are going to remember the nuances in what you are talking about in context. If you are talking about math for 60 minutes, continued references about math compete for people's memory. So when you want to anchor the audience to a concept, tie it to something very much unrelated to the topic you are primarily presenting on. For example, if talking about matrix multiplication, you might title the section "tic tac toe speed dating." It's a nonsense statement that you can weave into discussion about sequential translations of two dimensional grids that is just weird enough people will hear it through the noise of "math, math, math."

Then, you want to repeat the key point for that section again as you finish the section, and again at the conclusion of the talk summarizing your main points from each section, anchoring each summary around the heuristic you used. This technique is so successful I've had people I presented to talk to me 15 years later remembering some of the more outlandish heuristic anchors I used - and more importantly, the points I was tying to them.

As the audience member, the best way to save face on zoning out is to just structure your question as "When you talked about ____, it wasn't clear to me what my takeaway should be. What should I walk away knowing about that?" This way you don't need to say something like "I kind of got bored and was thinking about what I'm going to have for lunch - did I miss anything important?" Just "what should I know from that section?"

A good presenter will have padded the section a bit so summarizing what they think the main point was shouldn't take much time. It's also useful feedback for them as if you zoned out there, it's likely others did too so they might revisit or rework it if they plant to present it again.

And finally, most presenters should treat a question like that as their failure, not yours. If I'm presenting, it's my job to confer the information, not your job to absorb it. If I'm not engaging enough or clear enough in that conveyance, you bet I'd want to know about it. The worst thing to have happen as a presenter is zero questions at the end. By all means ask a question like "wait, wtf were you talking about in the middle there?" over just silently walking out to lunch bewildered, confused, and apathetic.

I struggle with this frequently. Of course, in many cases I waltz into a talk where (I think that) the rest of the audience knows more than me, and in those cases I don't say anything. The best solution I've seen is to first build up a ton of social credit and then ask tons of questions. I've seen a few cases of fancy professors asking very basic questions that I was too afraid to ask, and knowing that nobody thought they were stupid afterwards.

If you feel like you're in danger of giving this talk at the beginning, it might be best to explicitly say at the beginning that you encourage all questions, even if they're naive. I recall going to a talk where the speaker did this twice, lots of people asked questions, and I learned that the axes of a graph meant something different than I first assumed.

On the weirder side of solutions, you could try classically conditioning yourself not to take embarrassment so poorly. If you're a sugar fiend, bring some candies to a talk and eat one for each question you ask.

I also struggle with the fact that sometimes during a talk, I zone out and don't know whether the speaker already answered the question I have, precisely because I was zoned out when they might have answered the question. In this case, I tend not to ask the question, since I don't want to take the time away from other people listening to the talk.

Not an answer to your question, just an extended quote from the late Fields medalist Bill Thurston from his classic essay On proof and progress which seemed relevant:

Mathematicians have developed habits of communication that are often dysfunctional. Organizers of colloquium talks everywhere exhort speakers to explain things in elementary terms. Nonetheless, most of the audience at an average colloquium talk gets little of value from it. Perhaps they are lost within the first 5 minutes, yet sit silently through the remaining 55 minutes. Or perhaps they quickly lose interest because the speaker plunges into technical details without presenting any reason to investigate them. At the end of the talk, the few mathematicians who are close to the field of the speaker ask a question or two to avoid embarrassment.

... Outsiders are amazed at this phenomenon, but within the mathematical community, we dismiss it with shrugs. ...

Mathematical knowledge can be transmitted amazingly fast within a subfield. When a significant theorem is proved, it often (but not always) happens that the solution can be communicated in a matter of minutes from one person to another within the subfield. The same proof would be communicated and generally understood in an hour talk to members of the subfield. It would be the subject of a 15- or 20-page paper, which could be read and understood in a few hours or perhaps days by members of the subfield.

Why is there such a big expansion from the informal discussion to the talk to the paper? One-on-one, people use wide channels of communication that go far beyond formal mathematical language. They use gestures, they draw pictures and diagrams, they make sound effects and use body language. Communication is more likely to be two-way, so that people can concentrate on what needs the most attention. With these channels of communication, they are in a much better position to convey what’s going on, not just in their logical and linguistic facilities, but in their other mental facilities as well.

In talks, people are more inhibited and more formal. Mathematical audiences are often not very good at asking the questions that are on most people’s minds, and speakers often have an unrealistic preset outline that inhibits them from addressing questions even when they are asked. In papers, people are still more formal. Writers translate their ideas into symbols and logic, and readers try to translate back.

Why is there such a discrepancy between communication within a subfield and communication outside of subfields, not to mention communication outside mathematics?

Mathematics in some sense has a common language: a language of symbols, technical definitions, computations, and logic. This language efficiently conveys some, but not all, modes of mathematical thinking. Mathematicians learn to translate certain things almost unconsciously from one mental mode to the other, so that some statements quickly become clear. Different mathematicians study papers in different ways, but when I read a mathematical paper in a field in which I’m conversant, I concentrate on the thoughts that are between the lines. I might look over several paragraphs or strings of equations and think to myself “Oh yeah, they’re putting in enough rigamarole to carry such-and-such idea.” When the idea is clear, the formal setup is usually unnecessary and redundant—I often feel that I could write it out myself more easily than figuring out what the authors actually wrote. It’s like a new toaster that comes with a 16-page manual. If you already understand toasters and if the toaster looks like previous toasters you’ve encountered, you might just plug it in and see if it works, rather than first reading all the details in the manual.

People familiar with ways of doing things in a subfield recognize various patterns of statements or formulas as idioms or circumlocution for certain concepts or mental images. But to people not already familiar with what’s going on the same patterns are not very illuminating; they are often even misleading. The language is not alive except to those who use it. 

Okay, I liked that passage but maybe it wasn't very useful. Ravi Vakil's advice to potential PhD students attending talks seems more useful, especially the last bullet:

• At the end of the talk, you should try to answer the questions: What question(s) is the speaker trying to answer? Why should we care about them? What flavor of results has the speaker proved? Do I have a small example of the phenonenon under discussion? You can even scribble down these questions at the start of the talk, and jot down answers to them during the talk.
• Try to extract three words from the talk (no matter how tangentially related to the subject at hand) that you want to know the definition of. Then after the talk, ask me what they mean. ...
• New version of the previous jot: try the "three things" exercise.
• See if you can get one lesson from the talk (broadly interpreted). 
• Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind.

In research presentation, I'm always impressed when some of the brightest in the room have humbly asked the researcher to back up and explain something that others might find very basic but that's just a bit outside the questioner's domain. A speaker can tell when he's being asked something out of sincere curiosity. And rather than make me doubt the questioner's ability, it confirms it for me. It shouts confidence.

In groups that know each other well, I've also sometimes used humor to help ask the embarrassing question. Referencing the most-respected person in the room, I've sometimes said, "To help John here better understand (pausing and giving a wink to John), can you go back to slide 2 and explain how you got to step XYZ". It always gets a chuckle. And I get my answer.

When someone says that, I always use different words anyway, since its boring to use the same words.

Yeah, this sounds very reasonable. However, in a situation where the speaker won't take offense, I think specifying the reason for why you requested to repeat something could be nice. Sometimes people take "could you repeat this" to mean "could you summarize the last few minutes" or "I didn't understand, could you explain in more detail". Of course, this is a pretty minor cost, and it's better to ask someone to repeat things without saying why than to not ask at all.

Using repetitive speech can also cause people to zone out, irritate them, or make them think you're being forgetful.

Repetitive speech and other simplification tactics can also backfire. For example, if you try to oversimplify your presentation so that 'everyone can understand,' not realizing that a small core of fellow experts wanted and could have handled much more detail, while the majority weren't going to follow you (or care) no matter how much you simplified. If people then see you do this (performing pedagogy rather than inter-expert discourse), it can be seen as a misjudgment about the purpose of the event and the desires of the audience.

Repetitive speech has its uses, but it's important to be thoughtful about context, your goals, and the goals of your audience.

Interesting! Have you noticed that people repeat more or less than the past 20 seconds when you request that they repeat the past 20 seconds? I feel like I would find that more difficult to accurately measure 20 seconds of conversation than if someone told me to repeat everything I said after <particular talking point>. I don't think the difficult gap is huge, though, and I'm not sure if this is the case for most people.