So far have not found anything to solve this error: no connection or restarting the accessory, or reconnecting to the network, or restoring it to factory settings. Apple has not said anything about it. Most likely it's a problem with the servers of the company, as there are users of iOS 6 that can not start video FaceTime.
Some speculate that Apple has simply dropped the connection stating that AppleTV obsolete, but these measures tend to be preceded by a formal notice in sufficient time so that everyone can prepare. If you have one of those old AppleTV, better not touch anything and wait till the problem is solved.
