If a Google account keeps failing to authenticate in BlueMail, revoking the app's existing access and signing in fresh usually clears it.
- Open Google's third-party connections page and sign in with the affected account.
- Find BlueMail in the list and choose Remove access. That revokes the app's existing permission for the account.
- Return to BlueMail and update the password for the account. You will be taken through Google's sign-in again, and a new permission is granted.
If the error persists after that, remove and re-add the account.