Yes apart from upgrading to the latest version as @sunriseal suggested, also suggest to try “repairing your Gmail account” in eM Client to resync your mail folders. See the following thread for info - Force download of message that hasn't downloaded
If still won’t sync / download your some Gmail messages after repairing or upgrading, then if you are using a normal IMAP Gmail acct setup in eM Client (Non POP), then remove your Gmail acct in eM Client and re-add / setup as new.
Note - Before Upgrading, Repairing or Removing your account, make a backup first via “Menu / Backup”