Simulations are carried out to determine how polydispersity (delta) affects the potential energy surface of a colloidal system. Increases in polydispersity are shown to cause the disappearance of potential energy minima, such that energy minima corresponding to homogeneous highly ordered structures exist only for delta < 0.10, and energy minima corresponding to homogeneous partially ordered structures exist only for delta < 0.15. These results show that colloidal systems cannot form homogeneous crystals, even as metastable phases, above certain values of polydispersity.