Mine is doing the exact same thing, driving me crazy!!!
Not a DNS problem (220.127.116.11), not a .plist problem, not an AppleID problem, not a firewall problem, not a system or FaceTime re-install problem, not a router or wifi or ethernet problem. I've tried all the above.
Did you ever get this resolved? Thanks!
I called AppleCare yesterday to find out if my Logs had been analyzed and if they had an answer for my FaceTime issue. They did indeed have the answer. It was a "serialization problem". The original logic board in my Mac Pro 1,1 needed to be replaced, right after I purchased it, and the ASP didn't "serialize" the new board. The AppleCare rep told me to take it in to any Apple Store and they will serialize the board or replace it if necessary!!! And they refunded my $19.00 for Single-Incident support since it was due to an oversight by the original ASP! AWESOME!!!!!!!!
I shot over to my local Apple Store and within 5 minutes (FIVE MINUTES!) FaceTime was working!
Not sure if this will help anyone else, but paying $19.00 for AppleCare support is definitely the way to go, and you might even get it refunded!
This was a one week process, since my initial call to Apple, but they reviewed the logs and found the problem. The reps were all very professional and very knowledgeable. I can't say enough about this!! Very Happy!