Newly created games are not made active by default. Please make sure you set the game you want to play as Active before looking for it in-game.
You can edit a game by clicking the appropriate icon. Please note though you cannot edit or delete the Active game.

The host controls the game, and so for either joining and resuming the host should send invites out to players.
This is the sure-fire way of picking up a game where someone left from.