The phone I had with this problem needed to be replaced. A SIM card swap did not appear to resolve the issue.
My staff and I have come to the conclusion that all 83xx series BlackBerries are trash. We've seen all kinds of OS and hardware issues (including this problem) from the Curve that we've never seen with any other BlackBerry. I was initially very excited about the Curve, but after having used it for a while now I'm really disappointed with RIM (to say the least). It makes me very hesitant to buy the even newer ones like the Bold and Storm if RIM still can't get it right with a phone they've had out for over a year. AT&T is being far more helpful than RIM, so I have to give them props for that. Apparently someone (*cough*RIM*cough*) is getting a little too comfortable... given what appears to be abysmal product QA and lackluster support (which we pay for, for some reason)...
I might be switching everyone over to iPhones if RIM keeps sending us junk. :D AT&T was kind enough to provide a few Bolds to work with so we can try to determine if they're any more reliable than the garbage we have now. On the bright side, BlackBerry certainly isn't the only solution anymore, so if it doesn't work out they won't be hard to replace.