This morning I found the forcly stopped imapsync with a "Broken pipe" error message. I could not contact Zimbra using an IMAP clien or the web client.
On my Zimbra server /etc/init.d/zimbra status say that "mailbox" is stopped.
This relevant last lines in zimbra log say
2005-09-11 03:02:56,923 FATAL [ImapServer-2]  system - Fatal error occurred while handling connection
java.langOutOfMemoryError: Java heap space
Zimbra should handle such things more gracefully.