14 days. Hear me out:
There should be two checks, not just the last time you entered a move. First, the system should check the last time you logged in. Then check the last time you made a move. If the difference is greater than 14 days, you probably are not going to go back to that other game.
There could even be another check to see if you started another of the same type of game. Then that might show that you aren't going to return back to your previous game.