Crazy, I have exactly the same setup and the same problem.
The ethernet connected ATV (v4) always has access to the HDHR3-US Dual, never had any issues.
Recently introduced a second ATV over wireless (A/C). Channels found the HDHR right away and access was fine, few streaming dropouts as expected over WiFi, but generally very watchable (better than my antenna in that location).
But after a few days, the wireless ATV started reporting “HDHomeRun” unavailable when selecting a channel. Restarting the app didn’t help. Restarting the ATV would, although usually only for a short time (a few minutes). Restarting the HDHR didn’t help. Restarting the router (Arris Surfboard SBG6700-AC) would help, again for a limited time.
As with your situation, all other apps and functions of the wireless ATV seem fine, has internet access during these times.
One note when I first setup this wireless ATV it offered to update the firmware on the HDHR, which I did (to 20161117). I wish I had not, to see if this issue might be related…