This is a very interesting question and I will attempt to give you my humble theory.

From what I have studied of the Mongolian Tribes, they held numerous different strategies depending on what time they were in. But for the sake of clarity, I will refer to the strategies used during the reign of Ghenghis Khan at their height. Now first to find the chink in their tactical armour, we need to focus on their strengths.

One of the most effective tactics they used was the feigning of retreat. They won numerous battles with this tactic. One battle that stuck out for me was the Mongolian invasion of present day Georgia where they met up with Knights preparing to crusade. The Mongolian Army had traveled all day, met against superior numbers and still came out victorious. What made them effective was that they would feign retreat and the opposing army would break rank to pursue. The Mongols could turn 180 degrees mounted and fire arrows behind them and then turn and charge again without breaking their own rank. This then would cause a panic in the front ranks of the charging armies who would turn to run and hit the next rank behind them and so on. This caused complete chaos in which the Mongols would rain arrows and often lead to wholesale slaughter. This is incredibly hard to defend against and is still a relevant tactic of modern armies. It is usually alright when an army pursues but it is when they break rank that the issue begins. In the end, it comes down to discipline, strength and order of the army which was essentially unmatched with the Mongols.