Why do subtitles not work when streaming via AirPlay to Apple TV

To date, there are no 3rd party software implementations of AirPlay. The spec itself is fully patented (though most of these patents relate to the hardware aspects of the system) and is essentially a proprietary standard unique to Apple (though several hardware vendors have announced hardware that will use the standard - XtremeMac, Denon). The current analysis of the protocol itself seems to indicate that it is a further evolution of the previous AirTunes protocol (which itself was built on top of Bonjour), so you are likely to see software implementations appear after developers have had more time to experiment with the protocol.

No - that is not at all common.

Something is certainly causing the instability so you might need to isolate the potential causes one at a time.

• network issues (the most likely culprit but by far not the only one)
• Apple TV needing a restore or perhaps just a reboot.
• iOS device needing the same (restore or reboot).

Before restoring your iOS device, you might try the other steps first or also you could take your device to another network / Apple TV such as a retail store to test and make sure that's not the cause.