The other comments reflect speculation. Well-trod speculation (as in, it's mentioned in virtually every history), but nothing actually represented in the primary sources. I would point the other commentators to the Hunnic Empire, who succeeded in Eastern Europe with a very similar kit, so to speak, as the Mongols, but without siege engines or political organization.

I like Weatherford's book. I like Morgan's Mongols better. Saunder's History of the Mongol Conquests is also pretty good. There is also the invaluable Cleaves' translation of the Secret History, which is the primary source on the Empire, and really a remarkable text. Understanding the Mongols really takes several perspectives - somewhere between the apologists and the detractors is the disinterested facts, but they are hard to find.

The geographical argument, I think, is a terrible one, because there's not one instance where the Mongols were bested by European geography. The Mongols obliterated what forces were pitted against them in Poland, in Hungary, and in Austria, including crossing the Carpathians with a fighting force. The invasion didn't stop because Germany was an insurmountable challenge, the invasion stopped because the Khagan died in 1241. Mongol aristocracy elected the next Khagan by acclaim, and so the top commanders had to withdraw all the way back to Mongolia. This is the direct answer to your question: The Mongol invasion stopped for political reasons, not military ones.

Ogodei's death began the chain reaction which would cause the Empire's collapse. The next Khan, Guyuk, would ascend by political maneuvering and not by merit, and would alienate and finally threaten Batu Khan, the regional governor, so to speak, of Russia and the steppe.

Guyuk would devote himself to two fronts - the Abassid/Ismaili front in the Middle East, and continuing offense against the Song Dynasty. Guyuk had forces and commanders enough, even with the virtual loss of forces loyal to Batu Khan, to challenge two of the most powerful polities on the planet. No amount of woodland and hills can stop a war machine of that magnitude.

After Guyuk's death, the Golden Horde was closer to the fold with the success of their relative, Mongke. That said, Mongke had other problems at home. Two of the three branches of Chingis' succession planned a coup on Mongke, and he was forced to purge the Mongol aristocracy very early into his rule. Later he would put down revolts in Georgia, Turkey, and Kashmir.

His offenses neglected the Western border of the Empire entirely. He invaded Korea, who did not surrender to the Mongols, but negotiated peace instead. Dali, a kingdom in present day China, was conquered by Kublai and Subutai's son, who then sacked the capitol of Vietnam. The Mongol armies fell very ill to diseases of Vietnam's jungle climate, losing a major battle to the Vietnamese, but the king agreed to be a Mongol vassal, and the Mongol armies withdrew. The Mongols also invested in an extermination campaign against the Assassins and, after a personal slight to Mongke, razed the powerful and prosperous city of Baghdad. There were also some skirmishes along the border of the Delhi Sultanate. Finally, a serious campaign against the Song was lead by Mongke Khagan himself, with a second thrust from Kublai's armies. Mongke would become ill, and die, in China.

The following kuruldai would elect the administrator of Karakhorum, Ariq Boke, as Khagan. Kublai withdrew from China and waged a civil war against him, claiming the title of Mongol Khagan but losing any more than nominal control over the regional Khanates. Even so, Kublai would see China finally devoured by the Empire. If I remember correctly, in Kublai's time, Mongols ruled about 1/5 of all the inhabited land on Earth.

European geographic superiority is, in my opinion, a total illusion. The real truth is the Mongols were not interested. They ran rampant in Asia and the Middle East. Even the destruction of Baghdad, a traumatic event with a long memory in the region, is really a sidenote to the endless struggle against the Song, who the Mongols had a symbolic and historical rivalry against.

After the division of the Empire, Batu's heirs would struggle against the neighboring Ilkhanate, but mostly lord over the Rus, with seemingly little ambition. Arguments that they couldn't conquer Europe conveniently forget that, at the time, Europe was an absolute backwater compared to China or the Abassids, who the Mongols dispatched.

EDIT: I want to be clear, I have no horse in this speculative race. History is a very large story that isn't told in numbers of horses or the names of great commanders. If the Mongols had invaded Europe with their full brunt, I do not know who might have opposed them. But I also do not know how they would have managed a massive conquest a continent away from home. But the Mongols chose other fronts, it was not that rivers confounded them and so they turned tail.

One of the big factors that halted the Mongol armies where they were was the geography and ecology of the regions. Most of the Mongol conquests came on the back of their cavalry force. The average Mongol warrior had multiple fresh mounts to rotate, which lead to huge herds of horses. Those horses needed a lot of grass. Once the Mongols got to the heavy forests of Eastern Europe or the deserts of the Middle East, it became a logistical nightmare to try and feed all their horses.

Another factor was the way that the Mongol succession worked. Every time the current Khan died, all the princes and royal cousins, etc. would journey back to the capital in Mongolia to chance their arm to get chosen as the next Khan. The ones commanding armies in the west might not even make by the time a decision was made, but they went anyway, leaving their army in a lurch and less capable of taking on enemies. This was the case dramatically in the Battle of Ain Jalut. Hulagu Khan, the leader of the Mongols based in Persia down through Palestine, went back to Mongolia to make his case to be the Khan of the whole empire. However, once he left, the Mamluks from Egypt attacked north and defeated the remaining Mongol forces, stopping their advance permanently in the Middle East.