How Long Could Mars Hold its Breath?

Lewis Dartnell, A researcher with the UK Space Agency proposed that life grew on Mars, but some catastrophe stripped the planet of its atmosphere eons ago. That sounds like a great story, except that Mars lacks the gravitational pull necessary to hold together an atmosphere. Mars has only 11% of the Earth's mass. So why would Dartnell come up with such an outlandish idea? Because Mars shows signs of having once had an atmosphere.

Mars is covered with signs of past liquid water, and that requires an atmosphere with a pressure similar to our own. Valles Marineris, the largest canyon in the solar system, displays winding, branching channels indicative of water erosion along its edges. In 2011, ESA's Mars Express turned up more signs of water erosion. NASA's Mars rover has now determined high levels of liquid water exist a meter under the surface. All this could not be sustained under Mars' current atmosphere where water either freezes or boils. So Mars once had a substantial atmosphere.

But for how long? That's a question I pose to you physicists and mathematicians. Given Mars' low gravity, how long could it hang on to an atmosphere like that of Earth before the air would boil off into space? Here's my round guess: somewhere in the range of a hundred years, give or take several decades. You see, the best scenario to explain Mars is not that a catastrophe stripped it of an atmosphere, but that a catastrophe gave it an atmosphere, but the planet didn't have the gravity to hang onto it for long. I'm curious to hear your figures and factors.