Also, I have reset the network settings, rebooted it, turned it on and off, basically everything but another restore. But I feel like that wouldn't help either.

I bought an iPhone 4 from a friend and at first o had to restore it at the apple store because the phone had been disabled because they didn't remember the password, and after it had been restored it was working fine for about 2 weeks and now it would lose signal/service and it would come back...