The open stadium billiard has a survival probability, P ( t ), that depends on the rate of escape of particles through the leak. It is known that the decay of P ( t ) is exponential early in time while for long times the decay follows a power law. In this work we investigate an open stadium billiard in which the leak is free to rotate around the boundary of the stadium at a constant velocity, ?? . It is found that P ( t ) is very sensitive to ?? . For certain ?? values P ( t ) is purely exponential while for other values the power law behaviour at long times persists. We identify three ranges of ?? values corresponding to three different responses of P ( t ). It is shown that these variations in P ( t ) are due to the interaction of the moving leak with Marginally Unstable Periodic Orbits (MUPOs).