Apple Mail Forces Sign In Gmail

I struggled with the same issue after upgrade to Mojave 10.14.4. When I restarted the Mail app it worked well for some time but then some accounts got disconnected (happened with both GSuite account and personal @gmail account) Connection Doctor just said there was an error logging in to IMAP / SMTP with "invalid credentials" in the logs. However, it always reconnected just fine after clicking small reconnect icon next to each individual disconnected account. Then in an hour or two it silently got disconnected again, and again etc.

Eventually, I think I figured out what the problem was. I searched my Keychain and found [seemengly] duplicate entries for SMTP / IMAP / Google credentials for these "broken" accounts. Some of these entries held my latest passwords, however some held older passwords. I think in 10.14.4 something changed in how macOS picks credentials from Keychain, thus in some cases it started picking up older entries with outdated passwords. Anyway, after manually updating Keychain entries with the latest passwords I finally got rid of the problem.

P. S. I think deleting duplicate entries would also work fine. I just don't think they are really duplicate, but maybe used under different circumstances. Anyway, if deleted I believe you would be prompted for the new credentials when (if) needed.

Hope this helps!

Thanks. The Keychain suggestion straightened out my issues

see tutorial for login gmail : https://login-account.email/gmail-login-gmail-account-login/

Go to System Settings/ WiFI, and in the network you are using click the three dots. Then turn off "Limit IP address tracking."

Go back to mail, do the thing, then turn it back on.