I'm sorry, but none of this being a hardware issue makes sense. I use the 4:2:2 output and my box runs for days until the remote disconnects. And I am talking about watching 4K Dolby Vision content in the meantime, even 4K HDR 60fps. This past weekend, for instance, Fox broadcast their 2 NFL playoff games in 4K HDR 60fps and my remote didn't disconnect once. (Yes, I am affected by this pesky problem too - it's just that my remote was stable this past couple of days)
Let alone the fact that it resolves by simply rebooting tvOS, no need to unplug the box. If it were a more decisive interference, the remote would never work, or fail more quickly. Rebooting the software shouldn't fix hardware issues either. And if it were the case where the BT antenna on the box needed to be "refreshed"/"restarted" from time to time, they could do it via software too like a quick reboot of the BT chain, without having to reboot the entire tvOS. The remote would disconnect and reconnect almost instantaneously.