The beam-target interaction in heavy ion fusion is theoretically understood, but experimental verification at appropriate beam intensities is not possible using existing accelerators. If fusion-intensity ion beams were to lose significantly less energy in passing through matter than calculated it would increase the cost of heavy ion fusion. In the worst case the cost scaling is such that a 25% decrease in energy loss would increase the cost of the accelerator by roughly 10%. In this paper we show that fundamental considerations place a lower bound on ion energy loss. The lower bound is not significantly less than the expected energy loss obtained from detailed calculations.