I don't know what the issue is, it could be on the Android side. To test this, you could try running the app Enhanced Email (from Android Market) and see if that operates OK - if it does at least you can exclude it being a Zimbra issue.
Enhanced email used Activesync protocol to sync messages, contacts, appointments, but (generally) has more functionality and improvements over the standard client, as the name suggests. (No, I don't work for them lol

Good luck.