Whether extant life exists in the martian subsurface is an open question. High concentrations of photochemically produced CO and H₂ in the otherwise oxidizing martian atmosphere represent untapped sources of biologically useful free energy. These out-of-equilibrium species diffuse into the regolith, so subsurface microbes could use them as a source of energy and carbon. Indeed, CO oxidation and methanogenesis are relatively simple and evolutionarily ancient metabolisms on Earth. Consequently, assuming CO- or H₂-consuming metabolisms would evolve on Mars, the persistence of CO and H₂ in the martian atmosphere sets limits on subsurface metabolic activity. In this study, we constrain such maximum subsurface metabolic activity on Mars using a one-dimensional photochemical model with a hypothetical global biological sink on atmospheric CO and H₂. We increase the biological sink until the modeled atmospheric composition diverges from observed abundances. We find maximum biological downward subsurface sinks of 1.5 × 10⁸ molecules/(cm²·s) for CO and 1.9 × 10⁸ molecules/(cm²·s¹) for H₂. These convert to a maximum metabolizing biomass of ≲10²⁷ cells or ≤2 × 10¹¹ kg, equivalent to ≤10^-4-10^-5 of Earth's biomass, depending on the terrestrial estimate. Diffusion calculations suggest that this upper biomass limit applies to the top few kilometers of the martian crust in communication with the atmosphere at low to mid-latitudes. This biomass limit is more robust than previous estimates because we test multiple possible chemoautotrophic ecosystems over a broad parameter space of tunable model variables using an updated photochemical model with precise atmospheric concentrations and uncertainties from Curiosity. Our results of sparse or absent life in the martian subsurface also demonstrate how the atmospheric redox pairs of CO-O₂ and H₂-O₂ may constitute antibiosignatures, which may be relevant to excluding life on exoplanets.