My mac mail keeps asking for my google passwords every time the screen goes to sleep?

The security certificate is not from a trusted certifying authority.'

If so, you'll see a message that says, 'There is a problem with the server's security certificate. If your password isn't the problem, you may have a certificate error. See Change your password for more information.

Tip: If you want to change the password for your account with your email provider-for example, Gmail or iCloud-you'll need to visit the website for your email provider.