Okay, I have tested more. The laptop had nothing to do with it. In the meantime, had gotten to the point where I was getting no response at all, not even for one button-press. Went and got new batteries (the others were brand new, but perhaps not up to the challenge), Energizer Max. They seemed to do nothing, as well.

Went to this page at Nintendo: http://www.nintendo.com/consumer/sys.../wiiremote.jsp
and tried the un-sync and re-sync procedure there (wow, hold it for 15 seconds?!? I never would have thought to try that on my own), and I seem to be working again. So far, so good--I've played about half an hour and haven't had a problem so far.