A perennial ice cap has long been observed near the south pole of Mars. The surface of this cap is predominantly composed of carbon dioxide ice. The retention of a CO2 ice cap results from the surface energy balance of the latent heat, solar radiation, surface emission, subsurface conduction, and atmospheric sensible heat. While models conventionally treat surface CO2 ice using constant ice albedos and emissivities, such an approach fails to predict the existence of a perennial cap. Here we explore the role of the insolation‐dependent ice albedo, which agrees well with Viking, Mars Global Surveyor, and Mars Express albedo observations. Using a simple parameterization within a general circulation model, in which the albedo of CO2 ice responds linearly to the incident solar insolation, we are able to predict the existence of a perennial CO2 cap at the observed latitude and only in the southern hemisphere. Further experiments with different total CO2 inventories, planetary obliquities, and surface boundary conditions suggest that the location of the residual cap may exchange hemispheres favoring the pole with the highest peak insolation.