Why Did China survive for over 2000 years while the Roman Empire did not? 
During the First Balkan War in 1912 the Greek navy captured the island of Lemnos from the Ottoman Empire and promptly sent soldiers to every village and stationed them in the public squares. Children from all over the island ran to see what these so called Greeks looked like.
"What are you looking at?" one of soldiers asked. "At you Greeks" one of the children replied. "Are you not Greek yourselves?" said the soldier. "No, we are Romans" replied the child.
The above story was told by Peter Charanis, a well known historian, himself born in Lemnos in 1908. At that time, more than half of all Greeks still identified themselves as Romans and lived outside the official Hellenic Republic, in the Aegean, Thrace, but mostly in Asia Minor.
In the following decade, as the Hellenic Republic expanded and encompassed those areas as well (and eventually lost them in 1923), every child was taught to think of itself as Greek, not Roman. Thus ended the world's most ancient national identity, over 2700 years old since the founding of Rome.
However, if the original author is inquiring as to why there is a Chinese nation-state in existence today but no Roman nation-state, then the answer interestingly enough may be found in medieval and modern Greek history.
The gradual collapse of the western half of the Roman Empire forced the remaining East to redefine itself by a predominantly Greek population. Indeed, Roman citizens in the Middle Ages would commonly refer to themselves as Greeks as well as Romans and call their land Greece and Rome (Romania) alike.
This relatively homogeneous state with a sense of common identity among the people, stood in stark contrast to the earlier massive multi-ethnic Empire.
This is the defining characteristic of nationalism, which was growing all over Europe during the middle ages and eventually culminated with the French Revolution in 1789 and the world's first nation-state, France. In Greece proper and Asia Minor however, the totalitarian rule of the Ottoman conquerors hindered Roman nationalism from maturing and prevented it materializing in a Roman nation-state.
When the Ottoman Empire began dissolving in the early 19th century, the Roman people came together and finally did form their nation-state, which they named Greece instead Romania which was the de facto name the people used.
This break in tradition is attributed to the Renaissance on the one hand, which gave birth to admiration of the Classic era, and the increased reliance on the Great Powers for help on the other, who frankly found the prospect of aiding the descendants of Pericles and Leonidas far more appealing than helping the descendants of Basil and Constantine.
More importantly, by identifying themselves as Greeks, they renounced their claims to all and any Roman lands and titles their forefathers held, which put the great monarchs of Europe a little bit more at ease and inclined to help.
Still, once the political integrity of this newborn state was no longer at stake, the Greeks began a series of all out wars against the Ottomans anyway, in an attempt to reclaim all remaining Greek speaking territories in Asia Minor. Had they been successful, the final form of modern Greece would look surprisingly similar to the medieval Roman Empire on a map (The above is a real map published by the Hellenic Republic in 1920).
