The damaging effect of ionising radiation on cellular structure is one of the prime limiting factors on the survival of life in potential astrobiological habitats. Here we model the propagation of solar energetic protons and galactic cosmic ray particles through the Martian atmosphere and three different surface scenarios: dry regolith, water ice, and regolith with layered permafrost. Particle energy spectra and absorbed radiation dose are determined for the surface and at regular depths underground, allowing the calculation of microbial survival times. Bacteria or spores held dormant by freezing conditions cannot metabolise and become inactivated by accumulating radiation damage. We find that at 2 m depth, the reach of the ExoMars drill, a population of radioresistant cells would need to have reanimated within the last 450,000 years to still be viable. Recovery of viable cells cryopreserved within the putative Cerberus pack-ice requires a drill depth of at least 7.5 m.