The Mongols did go into India, they captured Kashmir and they made several attempts at the mainland. They didn't succeed in conquering into the Indian heart land for a simple reason, the same reason the Mongol's were unsuccessful in a capturing the Levant: They were repeatedly defeated by the Turkic empires that already existed in those 2 regions.
And in both cases, they were at a military disadvantage due to the climate of these lands. From my source:
Climate created the main impediment to Mongol campaigning in India. The Mongols’ livestock-raising economy depended on climatic—especially temperature--adjustments through nomadism to maintain the health and productivity of the animals, and the Mongol army, reliant on its horses, similarly depended on seasonally-adapted campaigning. The Central Asian campaign of which the first incursion into India was a part exemplifies this adaptation: the army operated in cooler highland regions in summer, and in warmer lowland desert and semi-desert terrain in winter. The Mongol wars with the Egyptian Mamluks over Syria exhibited the same procedure. The extreme heat of summer constituted the Mongols’ problem in India, as the quotation from Juvaini indicates. Their incursions seem to have been brief, even when not defeated by the forces of Delhi, and to have taken place in winter, because only then was it cool enough for the comfort of the Mongols’ horses (as, by the way, for modern tourists from temperate regions). The average temperature in the zone including Lahore and Delhi is 65-70 degrees F in November, and drops gradually to 60-65 at Delhi and below 60 at Lahore by February; thereafter it rises by May to over 90 degrees F. The Mongols did not want to jeopardize their horses’ health—and their own safety—by exposing them to this debilitating heat.
So the short answer is that they were defeated in battle, which is why they couldn't conquer substantial parts of India. For a more thorough answer, please refer to Mongol Armies and Indian Campaigns.