Amino acids are excellent biomarkers in the search for life on Mars because they are essential for biology as we know it and they are robust enough to survive for billions of years in the cold and dry Martian environment. However, amino acids and other organic compounds on Mars are exposed to the ionizing radiation from space and from the decay of radionuclides. This process and its role in the preservation of organic compounds has not been adequately addressed in the past. Based on measured radiolysis constants of amino acids and radiation dose estimates for Mars we show that the detection of an amino acid signature derived from an early Martian biosphere is not limited by its radiolytic decomposition as long as the amino acids are shielded adequately from space radiation. This indicates clearly the need to access the Martian subsurface in the search for molecular traces of an extinct Martian biosphere.