Martian wobble causes polar ice to migrate

The Earth has a distinct cycle of wobble (Milankovich cycle, among others) and now it turns out that Mars also has a wobble that changes the amount of ice at its poles. Every 51,000 Martian years (not Earth years... it'd be about 104,000 Earth years), the planet tilts so that one pole is much closer to the sun. The ice there tends to melt and eventually refreeze at the colder pole:

Mars, as it turns out, once had a propensity for juggling its polar ice caps from one end of the planet to the other.

A perennial wobble in Mars' tilt pushed one pole closer to the sun, causing water ice to evaporate and refreeze at the colder pole, new research shows. Every 51,000 Martian years, the wobble would bring the colder pole closer to the sun again and shuffle the ice cap back to the opposite pole.

www.space.com...

I read that article earlier and one thought came to mind.

The rovers and imagery from orbiters have proven the fact that Mars had much more water than it has now. I wonder if this cycle has been the cause of the loss of water on the planet ?

With the thin atmosphere and the planetary wobble, and including the gravitational pull of Mars, is this evaporation process how all that water could have escaped into space.

I researched abit and came up with this:

From Planetary Science

Escape of an Atmosphere
The thickness of a planet's atmosphere depends on the planet's gravity and the temperature of the atmosphere. A planet with weaker gravity does not have as strong a hold on the molecules that make up its atmosphere as a planet with stronger gravity. The gas molecules will be more likely to escape the planet's gravity. If the atmosphere is cool enough, then the gas molecules will not be moving fast enough to escape the planet's gravity. But how strong is ``strong enough'' and how cool is ``cool enough'' to hold onto an atmosphere? To answer that you need to consider a planet's escape velocity and how the molecule speeds depend on the temperature.

Therefore the chance of the vapor escaping from Mars is kinda unlikely, due to the fact that at Mars its very cold.OR it could be escaping, depenging on which of these factors is a bigger, well, factor. The pressure at Mars is around 6/1000 of Earth's, meaning its atmosphere is much, much thinner.