Well, they were basically a highly-mobile light cavalry/archers combination, so while they progressed very fast they were not spending much time sieging heavily fortified cities or going into mountains and other hard to cross terrains. Also it took Europeans a while to learn how to fight them efficiently, but eventually they did figure out that European heavy cavalry is a good match for them. So it's not they were "unstoppable", they simply avoided hard targets, and pillaged the villages and other less defended areas, and moved quickly through disorganized European kingdoms fighting each other.
That's not unique to the Mongols. Another easy example would be Alexander of Macedon. History is filled with great empires, many of them expanding, which fell or contracted after the leader passes.
PS. I wonder what - if anything - implications that has for leadership or management - you know, the whole achievement falling apart, missing one individual ...
(Or, to project management - low "bus factor", so to speak ...)
Basically unstoppable, eh? So, basically, an "accident" of history they did not take over the Mediterranean ...