We have employed a simple climate model of early Mars in order to estimate the duration of ice-covered lakes after the onset of freezing conditions on Mars. The critical parameter determining the existence of ice-covered lakes is the existence of peak seasonal temperatures above freezing. The peak temperature occurs at the subsolar point at perihelion. We use the weathering model of Pollack et al. (Icarus 71, 203-224, 1987) to compute the pressure and temperature evolution of the atmosphere. We have included the variability of the solar luminosity. We find that if there was a source of ice to provide meltwater, liquid water habitats could have been maintained under relatively thin ice covers for up to 700 million years after mean global temperatures fell below the freezing point. At this point, the mean annual temperature is 227 K, and the pressure of atmospheric CO2 is about 0.5 bar. Without the presence of stable bodies of liquid water, it is not clear what mechanisms were responsible for the removal of this remaining CO2. From a biological point of view, we find that the duration of liquid water habitats on early Mars exceeds the upper limit on the time required for the origin of life on Mars.