My understanding is that there is an issue in the way Cisco designed WMM and QoS on these routers. Wi-Fi Multimedia (WMM) is a wireless Quality of Service feature that improves quality for audio, video, and voice applications by prioritizing wireless traffic.
If you turn of WMM on these routers the 5GHz band stops working completely. 5GHz needs this to operate correctly. I believe this is where the issue comes into play. Something goes terribly wrong when both the iPad and Apple TV are on the 5GHz band and WMM screws something up with traffic passing between the devices.
So the work around I currently use is:
iPad (ver 1 and 2) on 2.4GHz
Apple TV on 5GHz
Everything works as expected with this implementation. Also, I have noticed that it is not only Airplay Mirroring that is affected, but everything when you are sending Pandora, Youtube, etc to the apple tv with both devices on 5GHz.
Let me know if that helps, I would also encourage you to read the forum comments as some others have work arounds that may help you as well. I have an E2500 and the same issue exists but the work around others used does not exist for my model. It may on yours.
http://homecommunity.cisco.com/t5/Wireless-Routers/E4200-with-Airplay-mirroring- hangs/td-p/456851