We just have setup ZD 2.0 for all users in or organisation for use with their Zimbra accounts.
On two or three systems ZD do not sync automatically for quite a long time, everytime user has to click 'Send/Receive' while the account has been setup for sync 'as new mail arrives'. It has been observed that when a user sends a mail, it remains in outbox until 'Send/Receive'. Similarly, new mails are also not received until 'Send/Receive'. This happens to almost all local modifications, are not two-way sync with Zimbra server.
I could not find any preferences or configuration to check on ZD for this issue.