If you're trying to prevent information-theoretic death by preserving the brain it's critical that the information that makes you be "you" actually be preserved. If you could freeze the brain in a way that did keep around the necessary information then some future civilization might be able to recover the person or the memories, but if the information is gone it's gone for good. The problem is, this is an untested medical procedure, and it's not something we should expect to get right flying blind.
In freezing a brain there are obvious things that can go wrong. For example, if you just cool it down to below freezing the water in the cells will turn to sharp little ice crystals, disrupting synapse structure and making a huge mess. We know about this now, though, so since the early 2000s cryonics organizations have used "cryoprotectants" which are able to vitrify the brain tissue and reduce  ice crystal formation. Beyond these known problems, however, there are many aspects of the brain structure that might or might not be relevant. Is information stored in the positions of proteins within the cells? Are phosphorylation states significant? What scale of preservation is sufficient?
Our normal approach is to try something, see if it works, fix apparent problems, and try again, each cycle getting us closer to something that does work. With cryonics the "see if it works" step isn't there, and there's only "check for known failures". So what we should expect is that the current process will be "good to the best of our knowledge" and then repeatedly our knowledge will expand about what matters and the process will need to be updated.
(Situations where current preservation technology fails to preserve something we know is required are actually kind of nice, because they're as close as we get to cryonics as an experimental science. Those are the cases when the process can actually improve because the feedback loop is temporarily closed.)
Imagine if in the development of In-Vitro Fertilization an inexplicable barrier stopped researchers from continuing any experiments past the "combine egg and sperm" stage. Instead they worked out something they thought was as good as they were going to get, documented it, and started freezing hopefully-fertilized eggs. How likely would it be that later we would be able to take these frozen eggs and complete the process? Much more likely would be that something unknown was wrong with the beginning of the process and these eggs would actually not be usable. Given that the brain is so much larger and more complex than these zygotes I expect the odds in the cryonics case are much worse.
Cryonics depends on a complex medical procedure developed under conditions of minimal feedback. Expectations for success like 80% or even more likely than not seem incredibly optimistic. When you can't test the output of a process because you don't know what counts as correct output it's very unlikely you've got the process right.
(I also posted this on my blog.)
 I say "reduce" instead of "eliminate" because as far as I can tell no one has actually taken random samples from a human brain that's been preserved with vitrification. There are ethical reasons why the cryonics organizations would not want to do this, but there being reasons why we don't wish to run a test doesn't mean we can act as if we already know the answer.