I have this problem with some mailboxes (actually Maildirs) on my system. After some user's activity there is following information in dovecot logs:
Jan 29 16:24:28 mailserv dovecot: IMAP(username): unlink(/var/spool/mail/imap/user/username/Maildir/cur/Sent:2,ST) failed: Is a directory User can not connect to his account neither via POP3 nor IMAP. There is one workaround I know which is: rm /var/spool/mail/imap/user/username/Maildir/dovecot.index* But after some time (some activity of user) the problem comes back. Mikie
