I would suggest to remove your Gmail account and re-add your Gmail account.
Note:- Make a backup first via “Menu / Backup”.
If still not working, then if you have any eg: optional firewalls / security programs, antivirus programs, vpn’s etc try disabling them (to test) incase of of them are interfering with eM Client connecting.
Lastly check what version of eM Client you have via “Menu / Help / About”. You may have an outdated version & needs updating. You can check for updates via the version history page - https://www.emclient.com/release-history