AirPlay option disappeared?
It's hard to say for sure, but I'm guessing there was a problem with the network discovery service. Apple uses Bonjour to advertise various network services (iTunes sharing, file sharing, AirPlay support) without the need to manually input configuration data. Unfortunately it can be a bit prickly at times, so if somewhere along the way the "Hey, I'm an Apple TV" message got lost, didn't get sent or received by your iPhone or Mac, it won't show up as an available device.

Unfortunately, the way Bonjour broadcasts the data seems to be a bit temperamental at times. I'm not aware of any real fix, but a restart almost always seems to fix it. If you're on a Mac, you can try restarting the daemon responsible by running the following two commands in Terminal:


sudo launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
sudo launchctl load /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist


But that will only fix things if the problem is the Mac not receiving the messages properly - if it's on the Apple TV's end, then restarting that is the best fix.