Seems I'm running to a "known issue" between Exchange 2007 and Microsoft's volume shadow service which performs snapshot backups of Exchange. Sometimes we get an Event ID 9840 which says that the snapshot could not be peformed because an aborted backup was detected.
What bugs me is that this is simply listed as a known issue and the fix in Microsoft's knowledge base article is basically "Yeah, just restart your mail server". On a production system, this is a completely unacceptable solution to the problem.
I can only hope that this is something to be fixed in a later patch or service pack but the article doesn't even give any indication that a fix is forthcoming.