Guys, I realize this is an old thread... however today, my old iPhone 4 FaceTime stopped working.
OS 7.1.2
I read all of everyones ideas, and accidentally found a solution for my phone in particular...
First the issue:
When using an iPhone 6 to call the iPhone 4 via apple id FaceTime, it would display "Connecting" indefinitely, then eventually CALL FAILED.
I tried this several times.
Then using an iPod which is using the same apple id as the iphone4, and this iPod connects flawlessly.
Solution:
Then I realized an easy fix by mistake... place a FaceTime Audio Call from the iPhone 6, to the iPhone 4, and wallah, it connected immediately.
Then do a video FaceTime connect, immediately!
My iPhone 4 is now capable of using FaceTime without any syncing or resetting, or losing app data.
I hope this works for someone else!
Let the community know if it works for you too!