There is a Chinese saying "The empire, long divided, must unite; long united, must divide. Thus it has ever been."
That saying has held true for most of China's long history. A great Chinese empire rises but eventually crumbles and fractures into many states. From the Warring spring and autumn period to the fall of Han and the three kingdoms, all the way to the fall of Qing and the warlord states in the 20th century. China always manage to more or less put it self together as a single Nation with a relatively consistent Chinese or Han culture at it's core since 206BC. Prior to the first Unification of China by the Qin, China was also divided into numerous states, many with it's own culture and ethnic groups. China ruled over a massive territory and population, no smaller than Romans. Chinese empires crumbled at the feet of foreigners and barbarians multiple times, from the mongols to the Jurchens to the Manchus. Chinese empires also crumbled from corruption, famines and internal instability; however, eventually it reunified.
After the crumble of the Western Roman empire, we have never seen Rome reunify (not counting the Holy Roman empire for obvious reasons), a nation having a majority of West Rome's territory with a distinctly Latin or Roman culture at it's core.
Why couldn't the Roman empire manage to put it self back together like the Chinese did? What was so inherently different about China and Rome that caused this? Why couldn't the former Western Roman provinces eventually reunify after the fall of West Rome in the 5th century?
I won't comment on Chinese reunifications generally, but I'd like to share my insights on the 5th-8th centuries, roughly the period from the collapse of the Western Empire to the rise of Islam, which corresponds closely with the Northern and Southern Dynasties, Sui and early Tang in China.
In both cases, we begin with two empires of roughly equal population and land area. Half of the empire (the Roman West and the Chinese North) is lost to foreign conquerors (largely Germanic peoples in Rome and largely Xianbei nomads in China). Roughly two centuries after the fall of one half of the empire, there is a major effort at reunification (under Justinian and Yang Jian/Sui Wendi, respectively) leading to short-lived successes but ultimate collapse. In Rome, the result was a rump Byzantine state but in China the result was a reunified and revitalized Tang empire. The general outline of events is similar but there were several critical factors that led to these different outcomes.
First, there is the question of geography and demographics. Although the total area and population of the two empires was comparable, the Roman Empire was marked by several distinct population centers linked only by sea- especially Italy, Egypt, Africa, Syria and Thrace; to a lesser extent the southern parts of Gaul and Spain- while the overwhelming bulk of the Chinese population was concentrated along a thin wedge bounded roughly by the modern cities of Xi'an, Beijing and Nanjing. The North China Plain was absolutely dominant over the secondary population centers of Sichuan and the Middle Yangzi. Defensible terrain sometimes allowed Southern states to resist the superior power of Northern states, but Rome's broadly distributed wealth, resources and people was more accommodating to the emergence of numerous stable, regional kingdoms.
A second factor is in how the invading peoples related to the imperial peoples they conquered. In much of the former Western Roman Empire, Roman institutions quickly deteriorated- urbanism and literacy in particular- largely to be replaced with Germanic practices. In North China, the conquering Xianbei peoples were relatively eager to maintain and adapt Chinese practices and to integrate with the Han gentry. I believe this can be explained mostly by the relative weight between the incoming and indigenous populations- the farming peoples on Rome's European frontier were more numerous to begin with than the nomadic peoples on China's northern border. This larger total flow of migration also settled largely in the Roman Empire's less-urbanized regions, like Pannonia and the interiors of Gaul and Spain, whereas in China they flowed into the empire's demographic center of mass. The end result was that barbarian migration was less disruptive as a whole- politically, socially and economically- in North China than in Western Rome, and that China's Xianbei conquerors were more readily subsumed into imperial society.
(A West Roman exception would be the Ostrogothic Kingdom in Italy, which was minimally disruptive to the Roman order and in many ways modeled itself as a legitimate Roman exarchate- which is to say that the conquerors became most Romanized in the most urban, and most ideologically important, part of the Western Empire. There was a similar dynamic at play in the Sinicized court of Tuoba Wei, situated in the old Han capital Luoyang.)
Lastly, there were contingent factors that dramatically affected the former Roman Empire, with no comparable challenges for China. Justinian succeeded in reconquering the core areas of the western empire, but afterwards East Rome faced three crises in rapid succession- first the Plague of Justinian, which may have killed between a third and a quarter of the empire's population, then Khosrau II's devastating war for the Near East, which nearly toppled Constantinople, and lastly the rise of the Arab caliphate, which again nearly destroyed the eastern empire and permanently pulled the Near East and Africa out of the Roman sphere. There were no comparable forces acting on China during the Sui reconquest or Tang consolidation.
In the end, China was reunified by a Northern aristocracy that was of mixed Han and Xianbei ancestry, which wedded steppe martial traditions to Chinese state ideology. Both the Sui founder Yang Jian and the Tang founder Li Yuan came from this background. They used the superior resources of the central plains, and the political support of the Han and Xianbei gentry, to maintain the empire's territorial unity. Qin-Han imperial ideology not only survived invasion and partition, it won the support of the invaders. Meanehile in the Roman Empire, Roman imperial ideology lost out to Germanic kingship in the west and to Islam in much of the east.
While more can be said on this subject, user /u/qewryt previously compiled a large list of answers on this subject that can be found here
Here's a direct quote of the links provided:
Some previous related questions:
Why have the histories of China, the Middle East and Iran seen more imperial unification compared to the history of Europe? How come China would fall apart and reunite, while Europe (Rome) fell apart and fragmented permenantly?
How was China able to not break up into small, European style countries?
Somewhat less related questions:
Is it fair to say that "Chinese civilization" is more "continuous" than "Western civilization"?
The list itself is about 4 years old, and there may be newer answers to these questions.