Greetings, micrographix.
We see that you reached out to us using the following resource: If Mail on your Mac keeps asking for your password
Were you able to review the information provided in that resource? Specifically, the section below:
“Check your password in Internet Accounts preferences
Depending on the type of email account you're using, you might be able to correct the password as follows:
- Quit Mail. If it doesn't quit, you can force it to quit.
- Choose Apple menu > System Preferences, then click Internet Accounts.
- Select your mail account in the sidebar.
- If you see a password field for your account, delete the password and type the correct password.
- Close System Preferences, then open Mail and try using your account again.
If Mail still asks for your password, the password is probably incorrect. Your email provider can help you verify your email settings and make sure that you're using the correct password.
Test using webmail
Many email providers offer webmail, which is a way to use email with a web browser such as Safari, instead of with an email app such as Mail. For example, if you're using an iCloud Mail account, you can use iCloud.com to send and receive email.
Because the password that you use with Mail is usually the same password that you use with webmail, try signing in to webmail with that password. If it doesn't work there either, your password is probably incorrect. Your email provider can help you verify your email settings and make sure that you're using the correct password for the Mail app.”
We ask because these steps will help isolate the issue. What happens when you log in to webmail?
Best wishes.