FaceTime Failed: Person Not Available
According to Apple, some of the symptoms are:


When you are calling someone on FaceTime, the number on their screen
is not your number.
People are unable to initiate a FaceTime call
with you. 
After installing a new carrier settings update, FaceTime
does not activate.


How to fix:


In Settings > Phone, turn FaceTime OFF and turn it back ON again
Go to Settings > General > Reset > Reset all settings
Done