Do you wear the watch loosely on your wrist? The Apple Watch locks when it thinks it’s lost contact with your wrist. Tightening up the band a little may stop the repeated log in requests.
I do not wear the watch loose. It is not overly tight, but also not flopping all over my wrist. I did update the watch OS recently, and the messages started after that.
Will the same thing happen if your wrist isn’t moving around, such as when you’re watching a movie or TV show?