I have the same problem.
The facetime was working for a couple of days after iOS6 update.
I updated my iPhone 4 to iOS6 on the 20th Sept 2012 (thursday). Facetime was fine until Friday (21st Sept 2012).
When I tried on Sunday (23rd Sept 2012), I started getting the CONNECTION LOST message. Now none of my outgoing messages on Wifi is working. iMessage, Mails with attachment, FACETIME nothing works on Wifi.
The speed of upload is ZERO when I test the speed through the SPEED TEST app.
I reconfigured the Internet Connection, but the problem still persists.
My laptop works just fine over the same internet connection and same Wifi settings. I can attached and send mails through my laptop but not through my iPhone 4.
Can any one help me on this?