Mongke (Genghis's grandson) took over when he died and became Khan. Mongke gatheered together his army and formed a huge assualt on the middle east. Baghdad was attacked and sacked again. Eventualy Mongke died and there was a power struggle between another grandson of Genghis and another member of the royal family, Arigh Boke. Their struggle weakened the empire. By the time a winner emerged the empire was now weakened beyond repair and was starting to fall apart. Certain areas became independant. The Yuan Dynasty started at this point.

Judging by what happened in this scenario and what happened to many other empires, there are only certain kinds of people who can control and maintain such vast amounts of power and wealth. Most people eventually become corrupted by wealth and power and forget about their loyalty to the empire, letting it decay and collapse.