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Intermittent problems are often a result of interference. Interference can be caused by other wifi networks in the neighbourhood or from many 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 that cause interference.
Refer to your router manual for instructions on changing your wifi channel or adjusting your multicast rate (which may help where interference is present. You might also try moving the Apple TV away from other electrical equipment.
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 or from device to device, so just because it worked before or works with a different device doesn’t exclude interference as a problem.
The following article(s) may help you.
Troubleshooting Wi-Fi networks and connections
Wifi Diagnostic Software (for Mac users)
You may also find some help on this page, where I’ve collected some of the more unusual solutions to network issues.
I understand that some of the suggested software (whilst once free) has become pay-ware, I suggest you look around, you may find free alternatives.
Apple TV HomeKit Disconnected
