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Large alluvial fan deposits on Mars record relatively recent habitable surface conditions (less than or similar to 3.5Ga, Late Hesperian - Amazonian). We find net sedimentation rate <(4-8) m/yr in the alluvial fan deposits, using the frequency of craters that are interbedded with alluvial fan deposits as a fluvial-process chronometer. Considering only the observed interbedded craters sets a lower bound of >20 Myr on the total time interval spanned by alluvial fan aggradation, >10(3)-fold longer than previous lower limits. A more realistic approach that corrects for craters fully entombed in the fan deposits raises the lower bound to >(100-300) Myr. Several factors not included in our calculations would further increase the lower bound. The lower bound rules out fan formation by a brief climate anomaly. Therefore, during the Late Hesperian - Amazonian on Mars, persistent or repeated processes permitted habitable surface conditions.