Constant demand for password in mail. Can't change,

I have 3 email (gmail) accounts. The primary one is ok.

the other 2 CONSTANTLY demand a password. I attempted to change all 3 to the same password.

Now the primary password field is populated with the old password, & the other 2 are blank. I add a password, save it when asked to save changes, & it immediately asks for my password when I long in & will not accept the new password, & constantly demands a password, & accepts the OLD one.

I open mail preferences, & on these two accounts, both password fields are blank.

Any one know how to fix this?