There does seem to be a problem with LDAP, but that might be a symptom rather than a cause: if the CPU is running at 100% then LDAP can't function. Here is another clip from /var/log/zimbra.log
But what is really strange is that zimbra functions fine for up to 5 mins, delivering and receiving email before it dies. It goes out so suddenly that even though I am running top to check which processes are using the CPU, top dies without showing the culprit.
Aug 10 13:40:50 mail postfix/trivial-rewrite: fatal: proxy:ldap:/opt/zimbra/conf/ldap-vad.cf(0,lock|fold_fix): table lookup problem
Aug 10 13:40:50 mail postfix/proxymap: error: dict_ldap_connect: Unable to set STARTTLS: -1: Can't contact LDAP server
Aug 10 13:40:50 mail last message repeated 2 times