I have exactly the same problem. Running a Macbook Pro with MacOS 10.7.4, iTunes 10.6.1 and up to date Apple TV 1st gen.
I have also tried factory restore of Apple TV, restarting MBP and router, but with no luck.
Currently I am running a wireless network directly from a D-Link ADSL modem/router. Will connect Airport Express to modem and let that create the network to see if it resolves the issue.
Any other ideas in the meantime?
I currently run all my Macs but one off a wireless network that consists of an Airport extreme and two Airport express units that extend the range of my wireless network. The reason I believe it is a bug in this particular O/S combination is because the Apple TV will show as a device in iTunse 10.6.1 on the Macs that are running O/S 10.5.8. The problem is that the iTunes library I want to Sync is on the Mac running 10.7.4.
I just updated to iTunes 10.6.3 and it hasn't fixed the problem.
It now appears to be associated with the Mac mini running the 2.4 GHz Intel Core 2 Duo. I have another Powerbook running the same MacOS 10.7.4 and iTunes version (10.6.3) but it has an Intel i5 processor and I can see the Apple TV in iTunes on that computer.
Have you tried logging out of the iTunes store and logging back in on the AppleTV? The AppleTV needs to be relinked.
Another Link: http://support.apple.com/kb/HT1143
You would be better off posting on the AppleTV index.
Appreciate the comments and I have done a bit more reasearch. I have eight computers on the network. Six Macs and two PCs. All but one have iTunes on them. Of the six that have iTunes, the two Macs running OS 10.7.4 and iTunes 10.6.3 (25) do not see the Apple TV when I attempt to connect to a computer from the Apple TV. The other four Macs see the connect request in the devices on iTunes. The Windows PC running Windows 7 on an AMD processor and iTunes 10.6.3 can also see the connect request.
Of the two systems running MacOS 10.7.4, one is an Intel Core i5 and the other is an Intel Core 2 Duo. Baring some other evidence, my conclusion is that there is a problem with the MacOS 10.7.4 and iTunes 10.6.3 combination.
Fall back position is move my iTunes and iPhoto libraries back to my older Mac mini and sync the AppleTV to that computer.