Thanks for using Apple Support Communities.
When connecting to or using a Wi-Fi network with Apple TV, you may occasionally encounter the following issues:
Unable to locate a Wi-Fi network
Intermittent disconnects or connectivity issues
For more information on this, take a look at this article:
Apple TV (2nd and 3rd generation): Troubleshooting Wi-Fi networks and connections
Troubleshooting AirPlay and AirPlay Mirroring
Best of luck,