  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, $\omega$. It is found that $P(t)$ is very sensitive to $\omega$. For
certain $\omega$ values $P(t)$ is purely exponential while for other values the
power law behaviour at long times persists. We identify three ranges of
$\omega$ 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).
