The "Limelight" is not established by those "whipping" him; he's establishing it himself by intentionally drawing attention to himself
His move to Harlem, his setting up the organization with Dole; Bill Clinton is continuing to make himself a part of the ongoing news and if he cooses to do that, then he's still in the limelight and still subject to criticism as an active player. If he would move himself off stage like most ex-Presidents, then he would probably not be under as much focus, but it's *his* decision to step back on stage