Having changed my Google password I now cannot update it in eM Client. When I open eM Client all I get is a dilogue box that says “Password required for firstname.lastname@example.org. This operation may take a while to complete. Please be patient.” which just cycles ad nauseum!
If your account is setup as IMAP, I suggest removing it from eM Client then adding it again. That will go through the 0Auth setup again. After entering your details a web page will open prompting for your account, so if it appears nothing is happening, check that the browser is not waiting for a response from you.