When it’s in this not-connected state, does it think it’s connected to anything else?
I ask because of a common problem in Apple’s Wi-Fi (especially phones) where it won’t switch away from an established connection without explicit action.
For example, if I configure my phone for my home LAN’s SSID and also Comcast’s “XFINITY” connection (for Wi-Fi roaming), I end up with problems whenever I come home after going out. When driving through my neighborhood, it will connect to XFINITY, since it finds connections from neighbors’ routers, but when I get home, it remains on XFINITY (which has much less bandwidth than my own connection). It won’t switch away unless I explicitly change my connection.
This got so frustrating that I told the phone to forget the XFINITY service altogether (and removed Comcast’s security profile, since that makes sure XFINITY is always on the list of allowed networks).
I’m wondering if you might be experiencing something similar. If your home LAN is a bit flaky (or maybe gets disconnected when you run the microwave oven before dinner), then maybe your Apple TV ends up connecting to a neighbor’s public access point, meaning it won’t connect to yours without explicit action. If so, then the solution is to edit the list of acceptable SSIDs (if it’s available to edit) and remove all but your home LAN from the list.