Hi guys,
I encountered the same issues and finally cleared it with the following resolution:
- Reboot your Wi-Fi router.
- Turn on your "Airplane mode" in your iOS device and then turn it off.
That's all. This method is safe and you don't need to change and initialize your devices. This was successful on my iPod Touch (5Gen) plus Remote app + AppleTV (2Gen) + the latest iTunes on MacOS X Lion.
If possible, update your AppleTV's firmware and iTunes to the latest as well.
If the issue persists, try unregister/register the AppleID on your AppleTV/iOS device/iTunes. (I believe this may be unnecessary in most cases).
I guess that some new iOS6 packets that relates to AppleTV and AirPlay sometimes disturbs by some Wi-Fi routers. Thus rebooting the Wi-Fi router catches and passes the new packets from iOS6 devices and clears the issue.
I'm unsure why turning on/off the Airplane mode clears the issue. This looks a small discrepancy in the new iOS 6.
Note that this is just my speculation.
Cheers,