We use a general circulation model to simulate the role of dust devils on the Martian dust cycle as a function of orbital precession. We focus specifically on the two most recent epochs of 22,500 and 72,500 years ago when perihelion occurred near northern summer solstice. We find that dust devils dominate the dust cycle at these times and that while orbital precession does modulate the exchange of dust between the hemispheres, the integrated effect is a net transfer of dust from north to south. The low thermal inertia continents of Tharsis, Arabia, and Elysium are the main regions that contribute to the net loss in the Northern Hemisphere and this loss is primarily due to dust devils. These results suggests that the dust cycle is closed on time scales longer than those associated with orbital precession (~50,000 years) and that obliquity variations must also play an important role in the long-term dust cycle.