The most common reason this will happen is because your server certificate is expired. To resolve the issue, do the following:

Renew your self-signed certificate for Zimbra deployment:

Stop all Zimbra related services (if not already done):

~]# su - zimbra
~]$ zmcontrol stop

Next, create a new Certification Authority:

(Note that from now on, following commands must be run as root)

~]# /opt/zimbra/bin/zmcertmgr createca -new

Now, create a new certificate. Set the expiration time to 3650 days (10 years):

~]# /opt/zimbra/bin/zmcertmgr createcrt -new -days 3650

Now deploy the cert and the CA:

~]# /opt/zimbra/bin/zmcertmgr deploycrt self
~]# /opt/zimbra/bin/zmcertmgr deployca

Finally, check the deployed cert:

~]# /opt/zimbra/bin/zmcertmgr viewdeployedcrt
::service mta::
notBefore=Jun 11 15:08:23 2012 GMT
notAfter=Jun 11 15:08:23 2022 GM

You should now be able to start all services including LDAP, without issue.