Clam shell mode with Apple TV & MacBook Air

I am presently using a HP2311x monitor, connected with a DVI cable. Works good. I was hoping to us an Apple TV with the monitor and MacBook air in clamshell mode. It works while the MBA is open but goes back to the usual Apple TV home sceen when I close the MacBook. I have tried different settings, like setting the display to "NEVER" sleep, but still I loose the MacBook Air desktop when I close the cover. Is this typical, or is there a way to mirror my MacBook Air display to the monitor using Apple TV, with the MacBook's cover closed (clamshell mode)?