A number of iOS 6 users noticed that FaceTime stopped working a few weeks ago. Today, Apple released a support document that explains what happened and the only fix is to upgrade to iOS 7 if they can:
If you started to have issues making or receiving FaceTime calls after April 16, 2014, your device or your friend’s device may have encountered a bug resulting from a device certificate that expired on that date. Updating both devices to the latest software will resolve this issue.
If you’re using iOS 7.0.4 or later or iOS 6.1.6, this issue doesn’t affect you.
If this was an intentional “bug” to force more users to upgrade, it is a pretty slimy move, although on the other hand, iOS 7 runs well enough (even on an iPhone 4) that there is no reason someone shouldn’t upgrade, especially from the standpoint of security.