There's a lot of reasons to such a broad question. I'll approach this from just one direction since I imagine there are some people more qualified to approach this from other directions. Lemme talk a bit about geography though.

Geography plays a way larger part throughout all of history then people consider at first. In this case, consider the difference in geography between China and the Roman Empire. Both are/were huge, yes, but China is one solid land mass whereas Rome is a ring of land with a huge inland sea. It's a lot more difficult to hold together an empire separated by huge seas than it is an empire that consists of mostly land. For one, if you want to move a large army you need to also possess a large navy!

Another important point relating to geography is what is, or who is, around them. To China's east was the pacific ocean, and the only real threat in that direct was Japan, which historically was often in self-imposed isolation. The Indians obviously couldn't interfere with China since the Himalayas and Tibetan Plateau form a natural border between them. The people of South East Asia weren't strong enough to impose any influence into China since they've never been fully united themselves. To the west there's desert and then Central Asia, where compared to China very few people lived. The only real threat then was Mongolians and the Manchus, and neither of them served to really collapse China but rather helped it's national identity, since they formed the Qing and Ming dynasties which both encompassed huge parts of what is today China.

Rome on the other hand only really had the Atlantic Ocean as a non-hostile border, and not much of Rome bordered the Atlantic anyway. To the North were Gauls, Germans and Britons (barbarians would've been the term used at the time). Eastward were the Arabs, not to mention the Huns from the North East.

In short, Rome suffered from trying to establish and maintain a national identity while being challenged for territory on almost all sides, while China dealt primarily with internal conflicts. Both Rome and China fell, but when China fell they were left to their own devices and allowed to re-establish themselves, and when someone attacked it was really just someone else unifying China for themselves. Rome had no such luxury, and when they fell the enemies they had on all sides swept in to take what they could.

Another quick points. China though a large chunk of land benefited from strategic rivers, especially the Yellow River and Yangtze river, which made shipping and movement somewhat easier without really hindering movement around the empire. China furthered this advantage by building canals.