A couple suggestions...
you said something about all the ATVs? Are they all in use, or has one not been used for a while? Sometimes an Apple device that hasn’t been used for a while will ask for an Apple ID sign in, that may be one asking for DHCP over and over?
you could give it a static IP address somewhere at the end of the range where nothing else is usually assigned.
try restarting router to get new IP addresses for all WiFi devices. Or even, turn off router, restart all devices, then startup router again. Check all your Ethernet cable connections.
try a different cable, maybe cable has gone bad ...also, maybe there is interference where the cable runs, maybe an electronic device, power supply or power cable it runs over or near it? ...Cat6 cables are supposed to be better against crosstalk/interference.
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... Gigabit fiber would be great too.
Fiber has no issues with interference, but, it’s not cheap, is it?