Same problems here. Outlook 2007, Zimbra NE 5.0.10.
Daily on one machine, less frequently on 15 more (once-twice a week, could be under-reporting, or less volume). Outlook works, syncing seems to pop up, but mails never come. Restarting Outlook fixes the problem.
We also have it coupled with strange situation that some people, in some cases, don't see some (not all) appointments scheduled in company wide shared calendar(s). It is very erratic, at one point one set of people doesn't see an appointment in Outlook, but other can see it, then later another group doesn't see a different appointment and so on. They all can see their mails and appointments in ZWC.
This guys are power users, on lower volume everything seems to be working fine, however, lots of mail+lots of appointments+Outlook 2007=trouble for us
We've also scheduled upgrade for this weekend, and connectors will be upgraded during next week, so hopefully, it'll go away.