As the title suggests, add a button right next to the Okay, for the option to save the game.
This would also come in handy if a game got desynced, for the game to automatically save.
This would come in useful for example, if the host's power goes out and he has infrequent auto-saves, or something corrupts. You won't lose that save or huge progress.
Allowing auto-saves for both (or multiple) parties could also be an option.