I and my wife have had exactly the same problem after the 16 th April 2014.
Before that, both our iPads and her iPhone 4 worked flawlessly with FaceTime , all running I0S 5.1.1 which we had decided to stick to.
Now the connections we try to make or receive, show "connecting" then failed.
At first I thought that it might be a problem with our ISP, which is Orange France. Once before we had to change the default DNS Server to the google 8.8.8.8 to resolve a connection issue.
However, my iPhone 4s which runs IOS 7 goes thru every time, but now won't connect to the IOS 5 devices.
I can only conclude that the part of FaceTime connections that Apple runs, has had an inadequatly tested software update in the last few days.
So Apple, please fix ASAP
PS Since starting this, I have just received a call, tried to answer on the iPad , call failed! Was called again within a minute, this time answered it on the iPhone 4S, call went thru and talked for over half an hour.
It has to be Apple