Hi,
I do have the same problem and it started just after christmas. Facetime will connect and then before a connection is established, it will just tell me, that the connection failed. I have the same behaviour on my iMac and on my iPad. Neither any software or hardware has changed on my side nor on the side of my mom, whom I try to facetime. We did facetime almost on a daily basis for a year without any problems and the very same set up.
I have never been on anything else but Macs, MacSE in 89 was my first computer, and I do hate it, when things just don't work! I am starting to get really angry about this!
I am facetiming from Germany to the US, where my mom lives. Could that be an issue now, where we know, that the NSA is even spying on Angela Merkels cell phone? This might sound silly, but at this point, I am so clueless that any explanation would make sense.
Something that used to work just fine, doesn't anymore and there seems to be no solution for this. I am very frustrated, too!
BTW: Video chat via iChat does still work without a problem! Unfortunately, I don't have a computer at home anymore and there is no iChat for iPad, so I am stuck with Facetime.