Answer:
Most Empires of the World collapsed largely due to economic and military(security) challenges. The collapse of the Chinese Empire was due to overpopulation which translated to economic challenges.
Other Empires has their unique reasons for their collapse. The Roman Empire collapsed due to a sharp decline in its population as a result of the small pox disease that ravaged the empire.
This is why I believe that each empire had its own specific factors that resulted in its collapse.