How can I stop my Apple Watch for asking passcode repeatedly?

Did you try to force restart your watch by pressing and holding the Digital Crown and the Side button together for about 10sec, until the Apple logo comes back again?

Is "Wrist Detection" still enabled in Settings/Passcode on your watch?

Any chance there are tattoos underneath the sensor?

If not, erasing and pairing the watch again, setting it up as a new device would be the next step:

Unpair and erase your Apple Watch - Apple Support

Their might something blocking wrist detection on your Apple Watch like tattoos etc you could also turn of Wrist Detection which i do not recommend since it helps you keep your information safe but if you really want to on your iPhone go into the Watch App scroll down till you see Passcode press on it then scroll down till you see Wrist Detection then toggle it off