I have read through this and many other posts with similar issues.
ipad 2 at 5.1.1 and ATV2 with latest firmware
Airplay mirroring works between ATV2 & iphone 4S and airplay works between ATV2 & iphone 3GS/iTouch.
On ipad2, I can enable airplay & airplay mirroring and it works for several seconds. Then the AppleTV option disappears mementarily from the Airplay list and then reappears with AppleTV deselected.
I have done a hard reset of ipad2 and power cycled the ATV2 & router. I have a strong wifi signal from the router at the point of test so I don't suspect that is the issue.
When I bought the ATV2 around May, Air Play worked with the iPad2. After reading other posts, I am starting to suspect that the update of the ipad2 to 5.1.1 may have been around the time Airplay stopped working. Other posts seem to point to problems when this was loaded too.
Any ideas on other things to try are welcome. Otherwise hope this helps contribute to knowledge base for others having similar issues. With many similar issues reported with iPad2 and 5.1.1 with Airplay, I am hoping this gets resolved with next update.
Other comments:
Ipad 2 is a factory refurbished unit
16GB of memory
WIFI only model
Linksys Router