Was it simply too long a march for an army? Mongols managed to make it all the way to Eastern Europe and the Middle East, so I don't see any reason why they can't just march or ride around the western edge of the Great Wall. They also had naval capabilities (as shown during the Mongol invasions of Japan), so couldn't they have departed by ship off the coast of Northeastern China or Eastern Russia and to land anywhere south of the Wall's eastern end?