Well there's this option still:
I posted this somewhere else in relation to iCal issues, but it's worth saying here as well. If you just bought a Mac or Mountain Lion 10.8, then I'd recommend taking advantage of the included 3 months of free Apple support (longer if you got AppleCare).
Here's the English number for Canada: 1-800-263-3394
Post your results back to the thread please!
I recommend it if only to get the issue further on Apple's radar. I called it in and had a guy try to explain away the problem, or the blame at least. No matter what evidence I presented, the support technician would just say the problem is [insert non-Apple produce/service here] and wouldn't create a ticket.
As my first Apple support experience (outside of the Genius bar), I was really disappointed. Actually, I take that back, considering the Genius bar, it was right on par which is to say a disappointment. But I suppose I got to talk to someone at least. That's a vast difference from other companies.
Anyway, I resorted to BusyCal and the disappearing invites were no longer a problem. It's not as polished and it costs a bit, but it definitely works the way a calendar application is supposed to work. There's a beta for Exchange services right now which handles the Mac in a Windows collaboration environment situation quite well.
Apparently, there's a big overhaul of Calendar.app coming in Mavericks so my advice is to wait and see how that goes. Run it through the tests, if problems still arise, call it in within 90 days. Otherwise, watch for a BusyCal sale. I'm sure they'll have one around that time.