Update and sorry it took so long to post but Apple wouldn't let me log on to the community site using my email address. Got lucky and just tried my user name and it worked.
So I spent a ton of time on the phone over several days with an Apple Tech. Restoring the phone to my last update was no good.
However, restoring the phone to the original settings and perhaps my last save when I first upgraded from an iPhone to an iPhone 4 proved functional. Facetime worked. Naturally a bunch of vital stuff was now missing from the phone including Apps, Music, Pictures and really most pressing, all my messages (huge history). Emails were gone too (but I have them on my Mac). For me this was a huge issue.
I restored the last update (prior to reseting the phone) and recovered (happily) all of the above missing data minus emails (still OK). Facetime now failed again.
Phone rep tried working with me to move stuff to iCloud (messages, contacts) with the idea that I can recover these first, then update music, pictures and Apps via iTunes later. However, we never got the phone to recover the critical one for me ... messages. So I am not bothering with this right now unless someone has a great idea on how to get Facetime working some other way.
Each restore takes nearly an hour so it is time consuming. In the process, I restored (back to factory) twice and got Facetime working. But when I restored to my last save, Connection Lost.
I have to admit my dissapointment that Apple is so not-in-the-know on this. They were shooting in the dark. Based on the number of people commenting here and on other Mac sites regarding this, if one is to presume active posters represent a small fraction of a percentage of people who are really affected, this is not a small issue. Apple should have better access to resolution issues on this matter.
After Patent Loss Apple Tweaks Facetime and Logs 500,000 Complaints - Ars Technica
That is a link that explains in part why people are having connection problems with FaceTime. The only thing we can do is complain to Apple for not supporting their products.