"password required to enable apple watch to unlock this mac"

This is a safety feature. The same safety feature that when using Face ID, you occasionally need to use your iPhones passcode

This is to prevent that when someone has stolen your MacBook and watch, that they can keep on using it without the password

This doesn't just happen on initial boot up. It happens throughout the day.

It should not happen throughout the day. Once upon initial boot, after that, no that's not normal unless you were to not use that Mac for a prolonged period of time (days) the number of which Apple does not discuss.

All I have to suggest is to make sure all their respective operating systems are up to date (Mac, Watch, iPhone) and otherwise make sure everything is in compliance with Unlock your Mac with Apple Watch - Apple Support. There are a great number of system requirements.

Also, if you do nothing at all for a little while (perhaps a day or two) you may find that the "unlock" feature spontaneously starts working again. I have experienced that on more than one occasion. I ignored it for a while, and it started working. I did nothing. Prior to doing nothing, I exhausted literally every option I could think of: restart everything, un-pair and re-pair the Watch, signed out of iCloud... etc. Nothing worked so I gave up.

Finally if all else fails please contact Apple using the Get Support link above. It is not supposed to do what you're experiencing.