Q: Airplay mirroring

I have a new iMac. Bought it in July, 2012. It runs Mountain Lion.

I have an Apple TV. Model MC572LL/A. Software 5.1.1 (5433)

Airplay worked for the first few months. Then it disappeared.

There is no icon. The display setting states "No Device Detected."

I have rebooted and reset everything, including the router. I have tried the Apple TV both wired and wireless.

We are on the same network; in fact, I can access my photos (even brand new ones) through home sharing.

I cannot, however, airplay or mirror anything.

It doesn't work with my iPad 2 either.

Please help.