Excess ice with a minimum age of tens of millions of years is widespread in Arcadia Planitia on Mars, and a similar deposit has been found in Utopia Planitia. The conditions that led to the formation and preservation of these midlatitude ice sheets hold clues to past climate and subsurface structure on Mars. We simulate the thermal stability and retreat of buried excess ice sheets over 21Myr of Martian orbital solutions and find that the ice sheets can be orders of magnitude older than the obliquity cycles that are typically thought to drive midlatitude ice deposition and sublimation. Retreat of this ice in the last 4Myr could have contributed similar to 6% of the volume of the north polar layered deposits (NPLD) and more than 10% if the NPLD are older than 4Myr. Matching the measured dielectric constants of the Arcadia and Utopia Planitia deposits requires ice porosities of similar to 25-35%. We model geothermally driven vapor migration through porous ice under Martian temperatures and find that Martian firn may be able to maintain porosity for timescales longer than we predict for retreat of the ice.