Thanks guys.
I checked the ipodlounge link you gave me, Neil. Went to forums, and lo and behold, on the first page there is a long tread addressing this very issue:
http://forums.ipodlounge.com/showthread.php?threadid=54039&perpage=15&pagenumber=1
Seems like a lot of people are having this problem. I did a "reset" like a lot of them suggested, and fortunately, it worked! Although I'm a little concerned that this seems to be a problem with the iPod that resetting doesn't always fix . . . .