There have been some anecdotal reports online that have indicated issues with iMessage on iOS. Below I have a few fixes that may correct the problem. I ran into this personally with one iPad and one iPhone in the last few weeks. Both times I had to resort to deactivating and reactivating.
Some users have reported that turning their iOS devices off and back on fixes the problem, while others indicate that the solution has not worked for them. In testing with my devices experiencing difficulties, the following steps didn't fix the issue but could and are simple:
1. Turn off iMessage in Settings > Messages
2. Reset networking settings in Settings > General > Reset
3. Reenable iMessage in Settings > Messages
iMessages do not appear to be failing back to SMS when this happens either. They just eventually appear as a failed to send in iMessage. Or if it is right after an update awaiting activation will appear in the iMessage and FaceTime System Preferences panel.
If these procedures above don’t work. Download Red Sn0w to your computer and perform the following steps:
1.) Connect device via USB cable
2.) Open RedSn0w
3.) Click on Extras
4.) Click on Even More
5.) Click on Deactivate
6.) Phone will show activation screen again. Open iTunes on the computer
7.) iTunes should detected the device and attempt to activate it.
8.) Device will reactivate with new tickets and Push, iMessage, and FaceTime should go back to normal.
Hopefully this should resolve any issues you may have with iMessage or FaceTime.