To clarify, I've heard of many loss mechanisms for Martian water, but not any that are believed to be capable of eliminating it. That is why most estimates put Martian water at less than half the depth of Earth's oceans if put back above the surface in liquid form. Mars lower gravity means thermal energy can excite atoms and molecules to escape velocity easier, but Mars' greater distance from the sn balances this somewhat. A lack of magnetic field means solar and interstellar particles can knock off a significant part of Mars atmosphere by kinetic energy transfer. I'm sure there are others I don't know of or am forgetting but Mars cold greatly reduces the impact of the ones I mentioned and probably most others by trapping water in the more stable form of ice. A warmer Mars closer to the sun might have lost its water, a cold Mars shouldn't.

Regards,
Mark