According to Antti Ruotsala, author of Europeans and Mongols in the Middle of the 13th Century: Encountering the Other, in 1241 Mongol vanguards were approaching Vienna, and Mongol scouts were approaching Venice when news arrived that Ogedei Khan had died. This is after Henry of Silesia had been defeated in Poland on April 9, and Bela IV had been defeated in Hungary on April 11. Ruotsala says that Batu, the grandson of Genghis leading the expedition, had even started collecting taxes and minting coins in Hungary.
A bit of background before I explain why they didn't go further. When Mongol leaders died, the entire royal clan and the clans of important noble families had to gather at what is called a kurultai. There were essentially sacred elections. The Secret History of the Mongols doesn't make it clear how a kurultai worked, nor do the Yuan Chao Bao Shi, the Jama Al-Tawarihk, John of Plano Carpini's report, or any other source to my knowledge. The only thing we know for sure is that any male within the royal family could be elected Khan, and that every important male needed to be there.
So, when Ogedei died Batu dutifully turned around and allowed his army to go back to Mongolia. Batu himself, however, didn't go. He was the son of Jochi, Genghis' first child. Jochi was the son of Borte, Genghis' first wife. Right after Genghis (or rather, Temujin, as he was called then) married Borte, she was captured by a rival tribe. Nine months later, Genghis got her back, and she had baby Jochi with her. No one could tell if Jochi was the son of Genghis or some rapist, though. When Genghis was an old man, close to death, he had Jochi murdered to prevent any chance of him being elected Khan and the empire being torn by dynastic dispute.
But back to Batu. Batu was the most capable of the viable candidates by all accounts, but he was hampered by his ancestry and the enmity of Guyuk, son of Ogedei, and Batu's cousin. For five years between 1241 and 1246, the Mongol Empire was in a stalemate because Batu refused to come to the kurultai and see his enemy elected. Toregene, Ogedei's wife and Guyuk's mother, ruled the empire in the mean time, but she did not have authority to launch military campaigns. Hence, between 1241 and 1246 no further raids were launched into Europe.
However, in 1246, Batu and Guyuk worked out a power sharing agreement wherein Guyuk promised not to kill Batu and that the next Khan would come from the House of Jochi. Simultaneously, Pope Innocent IV (r. 1243-1252) sent an embassy under John of Plano Carpini to try to negotiate peace with the Mongols. Guyuk vigorously rejected the Pope's message and ordered him to come to Mongolia and submit to the power of the Khan, or else the Mongols would invade Europe.
The Pope of course declined to do so, but the invasion never came. Why? Because the shit hit the god damn fan. Guyuk was assassinated, and rather than electing a Khan from the House of Jochi, Mongke of the House of Tolui was elected. This sparked an all out civil war between the houses of the four sons of Genghis Khan: Jochi, Chagatai, Ogedei, and Tolui. The result was the implosion of the Mongol Empire, and a cessation of any aspiration of raiding into Europe.
One of the original points of invasions was to collect loot for themselves. If the golden horde had enough loot from sacking pre modern russia and parts of eastern europe then there would be no need to go further west. Furthermore western europe becomes more forested and less amenable to the open plains combat the mongols favored, and the climate may have been unfavorable to the glues that held their unique style of bow/string together. As sunxiaohu said the major reason is the death of the great khan back home, but after the civil disputes over the throne the main regiment of the golden horde would be back at the outskirts of europe once again with the potential to push forward.
One should ask why after the breakup of the major mongol empire did the golden horde not return to the task it had started? I don't actually know. Perhaps they were contented by their already fruitful conquests or perhaps they no longer had the force of arms to take more victories against european kingdoms. One should also remember that as word of the mongols spread people started to learn of mongolian fighting tactics and could better prepare themselves to counter them. The mamelukes successfully routed a regiment left behind to defend mongolian conquests in the middle east, and as time went on I believe more and more peoples would learn the best ways of fighting the mongols. Part of the reason for their early success in europe was that european style warfare had not seem nomadic warfare in a long time and was ill suited to defend against it, and no one believed in the new threat coming their way so little preparations were initially made against it.