NGrant and Ken, thanks for the ideas and info! Overnight I was thinking about it and realized I should try what I just now discovered you suggested, NGrant. Plug the JBL into the computer, make sure the JBL sees that and is on, then change out the batteries. Wait a few moments, tell the computer (running Windows XP at home) to release the device (computer sees it twice, once for the JBL's internal storage and once for the card I have in it), then see if the JBL remembers everything. I'll let you know.
Also, holding down the "on" button longer may be a good idea, Ken. I'll try that, too, if the above doesn't work or if I'm somewhere I can't use a computer.
ProDigit, as far as I know, the batteries aren't the problem (I use the NI-MH kind, called for by my recharger), but who knows? the JBL may be sensitive to something about them that causes it to swoon when I change the batteries.