There is obviously no single thing that stopped the Mongol invasions. Two significant contributing factors were the transition structure of Mongol leadership and the relative poverty of Europe at the time.

When a Khan died, a regent could temporarily step into place to keep the basics of the empire functioning, but they had limited authority to conduct large scale invasions, enact new policies etc. A new Khan needed to be elected by a gathering known as a Kurultai, in which all the major families had to participate.

Before Genghis Khan died, he nominated his son Ogedei to be his successor - but this still had to be confirmed by a Kurultai. In the interim Tului reigned as a regent. Genghis had four sons that each got administration over different territories in the Mongol homeland. These would eventually become four Mongol houses.

Ogedei had a long reign, but spent most of it concentrating his attention to the East. There was Mongol expansion to the West as well, however, and a large invasion force was amassing along the borders of Europe in 1241.

Here is where some confusion sets in. When Ogedei died, his wife, Toregene, took over as regent in the intervening period. The invasion force that had massed, ready to attack Europe, departed shortly after Ogedei's death. There is some debate as to whether they left to attend the Kurultai or for another reason. The timeline seems suspect - it would have been very difficult for the message of Ogedei's death to get to the troops before they actually started departing. But it's hard to imagine what else would have caused the troops to depart so suddenly.

While Genghis Khan himself nominated Ogedei to become Khan after him, there was no such clear cut choice after Ogedei's death. There was dissension between the probably next choice, Guyuk, and his cousin from a different house, Batu. Batu continually claimed he was unfit to travel to the Kurultai, but according to tradition the Kurultai would not be binding without the presence of Batu's house. Eventually these delaying tactics ran out and Guyuk was enthroned as the Great Khan, and expansion could start up again.

Unfortunately, Guyuk only reigned for two years. After this there was another long regency before Mongke became Khan for 8 years. Mongke did have large scale invasions during his reign, but they were focused on Islamic territories, which were much richer in material and intellectual wealth than Europe at the time.

By the end of Mongke's reign the Ilkhanate, the western region of the empire, had basically broken off completely. The now fractured Mongol Empire did not have the same kind of expansive force as it once did, and possibly more importantly, the rulers of the Mongol territories had become significantly influenced by the way of life of the people they conquered, making large-scale mongol conquest a thing of the past.

An important note during this whole time is that Europe was also simply not that attractive to Mongols at the time. Its deep, dark forests that were inhospitable to an entirely mounted army and provided little in the way of fodder for horses. And compared to Islamic territories and China, it was backwards and poor. It's kind of like if you invaded the United States right now and took New York, Boston, and Philadelphia, you might look towards expanding your Empire down the coasts before attacking the Appalachians. It's not that you don't want them - it's just that it's a lot of work for very little payoff.

So, Mongols had a rotating leadership of short-lived Khans immediately following Genghis's death, with long periods of regency in which a large-scale invasion was impossible. No Khan's first priority would ever be attacking Europe - it just wasn't worth it. None really lived long enough to get to that part of the conquest to-do list, and then the empire fractured into many different pieces and got noticeably lest Mongolian.

For further reading:

John of Plano Carpini. History of the Mongols.

Saunders, J.J. The History of the Mongol Conquests, Routledge & Kegan Paul Ltd

Halperin, Charles J. Russia and the golden horde: the Mongol impact on medieval Russian history (Indiana University Press, 1985)