Oh okay. I disable port 143 (imap) in favor of 993 (imaps). Does cyradm only connects to 143?
Cyradm wants to use port 143/tcp - AFAIK it doesn't support IMAPs. Try running an IMAPd for standard IMAP that only talks to the loopback interface. For more information on how, please check the archives or "man cyrus.conf".
Craig Ringer