I'd start by saying that the conquests of various steppe peoples over the millennia are not all the same. The Mongols got as far as Poland and Hungary and were a global empire. The Huns under Attila were thought to be more localized, but were able to make incursions into Northern Italy and had also subjugated parts of modern day Germany.

One answer that I have read is related to geography. European geography West and South of the Hungarian plain tends to be constricted and somewhat rugged. Particularly Northern Greece, Yugoslavia, Austria, Western Germany, Northern Italy, and Scandinavia. This results in there not being a lot of grassland for grazing compared to the vast steps of Russia or parts of Asia and even the Middle East. The lack of pasture creates logistics problems for large nomadic tribes, who were overwhelmingly heavy in horse cavalry in their army makeup and had to be able to support large herds.

Western Europe is also hemmed in by seas, the Baltic/North Sea to the North and the Med to the South. This further constricts avenues of advance for an invading force unless that force is proficient in amphibious operations, which steppe tribes typically were not. A favorite strategic move by the Mongols was to invade a country with multiple armies from different directions to confuse and overwhelm their enemy. Again, this is harder to do the further West you go in Europe, where the terrain limits the ingress points for large cavalry armies. That type of terrain can also favor densely packed infantry formations over wide ranging armies of light cavalry, further negating the usual steppe advantage. So extended operations for steppe people into Western Europe was a logistical and tactical challenge that they weren't used to. The geography did not play to their strengths.

I don't want to discount the actions of peoples in Western Europe in successfully checking steppe army incursions, such as the actions of Flavius Aetius against the Huns, nor the role of chance, such as the death of Genghis Khan just as the Mongol invasion of Europe was getting going. I'd also add that the Mongols at least are on record of being successful across a diverse geographic expanse. From the Russian steppes to the Middle East, and all through China and into Southeast Asia. Although the grazing in or adjacent to many of those areas was arguably superior to Western Europe.

All that being said, I think Western Europe was probably a uniquely tough nut to crack due to its geography and its relative distance from Asia. Perhaps just as important, it may not have been seen as that valuable of a prize by an empire like the Mongols, due to what they would view as its geographic limitations and lack of wealth compared to China or other Asian kingdoms of the day.