This question has ostensibly been dealt with in at least three different /r/AskHistorians threads. I have read through all three of these threads and have concluded that there are two main theories.

The first has to do with the Himalayan orogeny being a geographically impassible hurdle such that the Mongol Empire didn't gain access to the sub-continent until well after its zenith, at which point it was no longer able to exercise the kind of long-distance power that it had known in the past. The argument here is basically that the sons of The Khan, while competent, were not quite up to the task, especially when faced with large and highly organized Indian forces.

The second theory is that the Mongols could not deal with the sub-tropical and tropical conditions they encountered in the sub-continent and perhaps wisely, decided to stay the fuck away.

I don't have an opinion either way. My area of "expertise," such as it is, has to do with native California and parts of Central America.

Ultimately then, my question is this; why did the Mongols leave most of the Indian sub-continent alone? Was it because they lacked organization by the time they'd finally made it around the Himalayan orogeny, or was it because they simply could not deal with the entirely different tropical environment? Or was it due to a third reason that I have not considered here?