Q: Apple Mail keeps requesting for my password.

This article should help you If Mail on your Mac keeps asking for your password - Apple Support

This happens to me every once in a while. Maybe every few months or so. I have tried different things, but never found out why. Everything appears to be perfectly in order. Annoying but no big deal.

Solution: I just hit "Cancel" in the dialogue box that requests the password, and then quit and reopen Mail and I stop being bothered by password requests, at least for that Mail account. If it recurs for other accounts, I just do the same. When you do this Mail may crash sometimes. Just ignore that. Has no lasting effects.