Dear Kenichi Watanabe,
Your suggestion to just use sync mode rather than managing music manually is workable, and I guess that's what I'll do if the problem recurs. The thing is that now, having restored the iPod, it's working fine again. (By the way, the problem isn't with an older USB -- I have the most recent iMac model but one, I just haven't updated my profile here in a while. And there's not much point in testing it with a different port or USB cable, since now it's working.)
I've been trying to recall exactly what happened leading up to the problem. I ejected the iPod manually, and it was fine. A little while later, I used it for about 30 minutes, then shut it down for awhile, then when I went to use it again, it indicated that the battery was dead, which hardly seemed possible, even if I had been using it the whole time, which I hadn't. So when I got home again, I reconnected it to the computer, and it seemed fine, until I ejected it again, which was when I got the thing about it being in disk mode. I think there was a power outage while the iPod was connected overnight, so I'm wondering if this would have disconnected the iPod without it being properly ejected, and this is what's caused the problem, even though it didn't show up immediately. I don't think there's really anything more to be done, until or if the problem occurs again.
Once again, thanks your helpful suggestions.