Apple TV 4K keeps signing me out

Every week or two, when I turn on my Apple TV 4K (2nd gen) and try to play a movie or TV show, the screen suddenly displays a "Signing out" message and does exactly that.

I'm signed out of my Apple TV+ subscription and every other streaming app I'm subscribed to, and I'm forced to go through the laborious process of reentering my strong Apple/iCloud ID password using the Apple TV remote.

What could possibly be causing this recurrent and extremely annoying problem? The Apple TV 4K and all of my various Apple devices share one Apple ID with the same iCloud email address and password, and this auto-signout happens despite the fact that I have made no changes to my Apple account and have added or removed no devices to my iCloud account.