Why is it that you can never find an answer until shortly after you make a public announcement? Ah well, I found the problem, and everything is working perfectly again...
For the record, here's what happened. In June I had a drive crash, and had to restore all of the user folders from backup. For some strange reason, all of the restored files became owned by root. Roundcube (and thunderbird) were detecting that there were a number of files in the folders that couldn't be read, and seem to stumble over what to do in that case. In my situation, every folder that contained emails with permissions set to root, the first page of emails would be displayed in rcmail as a blank list. After a recursive chown, everything appears to be working great in rcmail again.
As a side note, I was also noticing incredibly long load times for every page (sometimes well over 1 minute) even though my server had very little load. This problem has now gone away completely, and I am seeing mailboxes with over 1000 emails loading in about 4 seconds. I am assuming that rcmail (or maybe my local courier-imap?) was hanging up trying to gain access to the mis-owned files.