I've seen a few things addressing this, but none seem to apply to my version of Zimbra desktop (7.01).
I set up zimbra specifically to deal with email from my online store. It tested fine, but at various times I get something from the "mail delivery subsystem" that, as far as I can make out, is telling me that a store email failed several spam checks.
I've long forgotten anything I ever learned about network admin. If anyone can help, please let me know what information you need, as well as "the button is here" steps to changing whatever is blocking (some of the time!) any of the three email addresses set up for my store.
I can check all of email in browser clients, but really liked zimbra in particular, and having a distinct desktop client, to monitor incoming orders, comments and issues.