Have you checked /var/log/zimbra.log and the log files under /opt/zimbra/log ?
The majority of LDAP issues are down to a mis-configuration of DNS. So once you check the logs please post
Code:
cat /etc/hosts
cat /etc/resolv.conf
dig yourdomain mx
dig yourdomain any
host `hostname` <- note backticks and not single quotes (copy 'n' paste)