I suspect most of the water went away when Mars was struck by the large rock that ripped off half its crust.
When did this happen? I know of the earth impact that created the moon, but am unfamiliar with such a Mars event.
Or maybe not a direct impact. The gravitational attraction of a near miss by a large rock (planet-size or nearly) could strip off almost all the water, very quickly, and leave one hemisphere of Mars very different from the other hemisphere, as it is now.