I've done a little poking around online, and I can't find anyone else who's had this exact problem, or even ones that sound similar. Which suggests that it might be some random third-party software problem, and the problem with diagnosing that is the inability to replicate the behavior -- I can't just remove things until the problem goes away, because who knows when it will happen again? I think my two choices are to either start from scratch or just live with it, and since I get the feeling the computer isn't badly endangered by the problem (like, not on the verge of death), I think for now I will live with it, and just get in the habit of saving important things before I sleep it, and of shutting it down overnight on a regular basis (which was T's suggestion). Then when I get back from my trip, I can think about reinstalling/upgrading/shelling out for AppleCare.
Oh well, at least I have it back. And I got actual good advice on the fact that my wireless has been so flaky as to be unusable for the last several months -- he just tweaked a setting, and I think that did it. I've been off the Ethernet ever since I got it home and it hasn't cut out once. So at least something has improved.