The growing thread about the problem in Apple's support forums started March 13, according to AppleInsider and has apparently affected dozens of posters. While the rebooting isn't rocket science, persistent problems may mean that the problem lies with Apple's iOS 4.3.
FaceTime, Apple's video-calling software, only works on iOS devices with a forward-facing camera -- basically the iPhone and now the iPad 2. So far, there have been no complaints about FaceTime on the iPhone.
Apple hasn't publicly commented on the problem, but if it is a problem with the iOS 4.3, the new update iOS 4.3.1 may alleviate it. The new fix is rumored to patch memory and could make a video-calling system run more smoothly.