Considering that the skeptics in the example you've outlined are mostly misinformed/uninformed due to misconceptions about AI, I find that skepticism is more of a natural response to uncomfortable assertions made by AI boosters ("It's coming for you!") than a fault in epistemology in the search for truth. It makes the most sense to me that the default position skeptics take is anti-AI, but with any suggestion that the technology is unable to improve, their position becomes that of a skeptic. For this reason I believe it'll be difficult to convince skeptics with logical arguments before there's clear evidence against their point, mostly because of their strong bias.