I had this problem when I setup the server before DNS;
Zimbra was setup on server.localdomain.local before setting up the DNS records pointing to mail.publicdomain.com and then creating the 'real' domain in zimbra. Zimbra was trying to deliver its 'internal' mail to
admin@server.localdomain.local; I created an alias for the admin account and hey presto - daily activity reports, AV/AS notifications etc. started arriving.
Hope that helps
Jon