If it doesn’t officially push the update on your computer normally, you just backup eM Client manually via “Menu / Backup” and the close eM Client once backed up and d/l the latest official release version via the history page and install.
I upgraded yesterday to 9.0.1708 (2cfb4a5) and now eM Client will not fully close, in the background is a notice “The application is uninitalizing.” Only by terminating the app session will it close so it can be launched again.