If it is recent, it might be overload of the FaceTime server as lots of new users try it out, though that sounds unlikely. Apple hasn't reported any outages in the last few days (though server overload might not count as an outage on their status page)
It might be a less than great internet connection as well.
You could try reseting it, sort of. Go to Settings > FaceTime. Tap your Apple ID and sign out. Wait a few minutes and sign back in. This sometimes straightens out problems, though I'm doubting it has anything to do with the symptoms you are describing.
Good luck.