I frequently get notifications from my Apple Watch saying to enter my iCloud password.

[half roost]

Every few days or a couple of times a day I have to put my iCloud password into my Apple Watch for some reason in the settings app.

This issue occurs again and again even after correctly entering my password and addressing the notification. There is nothing about it showing up on my iPhone.

[peak marsh]

I'd try unpairing and pairing the watch. That fixed it for when I had the problem

https://support.apple.com/en-us/108372