My guess is that Zimbra starts before before syslog on system bootup. Are you only seeing those errors when the system boots up fresh?
My answer depends also on which version of Zimbra you are using.
Two things to check on, both discussed
in this thread. (Not the same OS version, but similar and Zimbra 4.5)
1) See if /etc/syslog-ng/syslog-ng.conf has a few Zimbra entries in it. If not, you will need to add those (see the other thread for details).
2) You need to correctly tell Zimbra to start after syslog if it is not. See the edits to /etc/init.d/zimbra for details.
Quick check: Look in /etc/init.d/rc3.d/ and make sure that the S??zimbra file has a larger number than the S??syslog file. This tells zimbra to wait until the syslog has loaded before starting.
Again -- this depends on both the OS and version of Zimbra you are using.
Hope this helps.