What do you see when you look at the ATV network settings when it says it cannot connect? I expect it will list other networks, ** not yours. That will indicate that your network became unreachable, probably due to interference.
Have you checked for interference? Look out especially for cordless phones. You can get WiFi "stumbler" programs for computers and some phones that show the signal level of competing networks. I think the function is built in to OS X. You may find that you're sharing a channel with several others. And one of the interferers may only become active once in a while, killing your ATV. I'm in a suburban neighborhood with relatively large lots and I can see 14 networks!
Next time it happens, please try only restarting the ATV and see if that makes it work. I expect that it will.
There are WiFi frequency bands at 2.4 GHz and 5 GHz. The 5 band is less crowded. It is used by 802.11ac and can be used by 802.11n. See if your router settings allow this.
You should try updating to the brand new today tvOS 9.2.1, in case it includes a fix. Can always hope. Please report if that helps, since the world is waiting to know...