Sure enough there were a few pop3 processes sucking down 100% CPU loads. The log showed:
Nov 2 12:39:57 mail pop3(firstname.lastname@example.org): Timeout while waiting for release of shared fcntl() lock for index file /var/spool/mail-domains/domain.com/CEO/mail/.imap/INBOX/.imap.indexA quick look showed that there were multiple processes locking out the file. After some "duhs" I got the right processes stopped, killed the remaining, and restarted. No change. Restarting all processes involved also showed no change. The moment the user came in, things locked back up. Tried removing and rebuilding the IMAP files, no change.
Eventually, I came around to the old standby and I did a $ mail -f CEO/mailbox and then quit out. That fixed it. Still not sure why.