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