One way, which, I feel, can be tried is depicted in my hot backup script I posted a few articles back. I haven't had much time lately to work on it but will try to progress the idea. I can confirm that it backs up ... restoration is something on which thinking is required.
To trap incoming e-mails when the mail server is down ... have 2 mail servers running... Zimbra and some other (maybe another Zimbra) with different priority MX. When the first one is down... the second one picks up mail. When the 1st one is up... retrieve e-mails from the 2nd one - and normal service continues until the next time you want to backup.
Something like what this company offers:
(I don't know this company ... can't comment at all on its services, price, etc. Just came across while Googling)
BTW, if you are willing to pay for this service, better yet, is to get Zimbra Network! :-)