I am not looking to put anyone out of the game for a week of inactivity but I think that a 1 to 2 percent per day penalty would keep them active. I wouldn't impose it after 24 hours but after each subsequent 24 hour period and then I would reset the timer right after the player makes a new move. Of course there would have to be a way to verify that the player is playing and not just auto refreshing a page to show as active.. You already have activity script active in guilds.
Do you remember Clark Gable, Gary Cooper, Errol Flynn, Jack Lemmon, or Hal Riddle? They were all famous. Now nobody knows them. Why? Because they are not acting.