You'll find the log files here: Log Files - Zimbra :: Wiki You should also run the following commands to check your DNS & hosts file setup is correct:
and post the output (plus log file infor) when you've done your investigating. There are also likely to be threads in the forums that cover your problem, do a search for those. It also helps to know if you're on NE or OSS version of Zimbra and which operating system you're using. Run this command: 'zmcontrol -v' and add the output to your forums profile.
dig yourdonaim.com mx
dig yourdomain.com any