James Goodlet has identified the cause of the evil exited, signaled to death by 6 errors in Mac OS X Server. Really, it is a problem with the Cyrus IMAP server. Goodlet explains as well why the problem occurs when checking email with Mail.app and Entourage but not with Thunderbird. The short version is that the Cyrus IMAP server's reconstruct command rebuilds the message index with INTERNALDATE having a length of 0. This condition is illegal. Mail.app and Entourage request the INTERNALDATE attribute but Thunderbird and WebMail do not.
The long and short is this is a problem that has to be fixed on Mac OS X Server. It is not a client problem (there are other problems with Mail.app).