I am having the exact same issue. The Apple TV 4 is running fine so far but out of the blue the "No Network Detected" message pops up while the stream (iTunes movie or Netflix) still continues to play.
Oftentimes after switching the Apple TV on for the first time and then trying to watch an episode of a series it says something like "available in 1 hr 42 mins" or such. After a restart of the box I can watch the episode immediately.
The Apple TV is connected via WI-FI with a dedicated IP adress (settings in router and Apple TV applied). My DL speed is around 47 MBit/s, the network settings show 5 dots for the Wi-Fi connection quality, the router is about 3 meters away. The SSID is visible, MAC filter is active, Apple TV MAC address is in the "allowed" list. Router restarts and Apple TV reset both have been done.
I am asking myself if the issue occurs because the Apple TV is switching between the 2.4 and the 5 GHz connection, both of them have the same network ID which isn't an issue with my other Apple/network devices.
Is there a way to force the Apple TV to connect only to the 2.4 GHz connection without renaming one of the network IDs?