I didn't know it was broken
Apparently, there was some sort of urgent FaceTime fix – who knew? Not me, certainly, but apparently Apple did and has thus released a new version of their iOS 7 mobile operating system, dubbed iOS 7.0.4, which brings with it a fix for those apparently buggy FaceTime connections. Apple claims that they’ve thrown in a couple of extra bug fixes in there for good measure, but go short of explaining what those actually consist of – but we trust that things have been made better, not worse.
For those interested, Apple’s full release notes is as follows:
Bug fixes and improvements, including a fix for an issue that causes FaceTime calls to fail for some users.
For information on the security content of this update, please visit this website: http://support.apple.com/kb/HT1222
iOS 7.0.4 is available vita an OTA update for all compatible iOS 7 devices, including the iPad mini (both generations), iPad 2 and up, iPhone 4 and up, and iPod touch (5th generation). Have at it.