Welcome to the Apple Community.
The only requirement for AirPlay is that both devices are on the same network, have you checked this.
Intermittent problems are often a result of interference. Interference can be caused by other networks in the neighbourhood or from household electrical items.
You can download and install iStumbler (NetStumbler for windows users) to help you see which channels are used by neighbouring networks so that you can avoid them, but iStumbler will not see household items.
Refer to your router manual for instructions on changing your wifi channel or adjusting your multicast rate.
There are other types of problems that can affect networks, but this is by far the most common, hence worth mentioning first. Networks that have inherent issues can be seen to work differently with different versions of the same software. You might also try moving the Apple TV away from other electrical equipment.
A frequent cause of consistent failure to enable AirPlay or HomeSharing at all, is the service being blocked on the network. Make sure your network isn't hidden, has a unique name, that MAC address authentication is disabled, security is set to use WPA 2 Personal and that there is only one router/device acting as a DHCP server and providing NAT services.
Make sure your router/computer allows access over the following ports
Refer to your router manual/manufacturer for any settings that are specific to that model.
Another frequent cause of consistent failure to enable AirPlay or HomeSharing at all, is security software, in many cases configuring it correctly, disabling it or even uninstalling it can help, but in some cases the security software can cause problems that simply reconfiguring, disabling or uninstalling cannot reverse.
If you are consistently unable to activate AirPlay, have tried all the steps in this article and have security software installed on your system, you might benefit from contacting its provider or participating in any online forums they run to discuss the matter with them.