I would submit that part of the explanation is that China's perpetual continuity is a partial illusion. What we call China today has experienced remarkable periods of strength, territorial size, and regional hegemony, but it has also spent centuries split among numerous states. Between the founding of Qin and the founding of Song, China was "disunited" for about four and a half centuries, a not inconsiderable length of time. Peter Bol has argued it was during the Song that Chinese scholarly elites began to imagine China's natural state as "unified", and indeed, according to the Qing-era zhengshi, or "orthodox history", the Song, Yuan, Ming and Qing are accorded full historical chronicles.

However, (and this is getting into my own thoughts on Chinese historiography and the problems of latent national primordialism), I think we should imagine the Liao and Jin states, contemporaries of the Song, as Chinese states that existed in a period of disunion. The Yuan dynasty faced a historiographic problem themselves when their court could not decide which predecessor - Song, Liao, or Jin - to write a history for. In the end, a Muslim scholar suggested writing one for each, and the emperor signed off on the project, so now if you find a collection of all the zhengshi, it will include the Song shi, Liao shi, and Jin shi.

There are some explanations for why China unified and eventually reunited while Rome didn't, but they fall outside my era of expertise, so I'll refer to two quickly:

Victoria Hui, War and State Formation in Ancient China and Early Modern Europe. She argues that Qin and Han engaged in self-strengthening practices, allowing for one-state hegemony and eventual conquest, while early modern European states engaged in self-weakening practices that reduced the ability of the central state to maximize central control over elites and regional forces.

Jane Burbank and Frederick Cooper, Empires in World History, argue that elites in early China depended on the central state for wealth, power, and prestige far more than their Roman counterparts, ensuring Chinese elites were more amiable towards unification, because serving a larger, more prestigious state was better for their own status as well.

People here surely arn't fans of [A Certain Book], but the geography of China deserves some evaluation here.

To the south of China proper is dense jungles that expeditions by the various dynasties failed to exert control over. The tropical diseases and general conditions saw more than one army swallowed up into the mists; the Chinese state generally settled for exacting tribute from the nations over conquest. To the west is the formidable Tibetan plateau, which needs little explanation. North, the endless expanse of mongolia and the land of the eternal bane of China, the steepe nomads. Korea is a tiny little nub also famous for destroying an entire dynasty after it overextended militarily into the peninsula. China therefore holds very natural borders that it's powerful dynasties settled on holding, with very little value in seizing more. The notable exception is Xinjiang, along the silk road through the Taklamakan Desert, which was a profitable route to the more western empires of the Persian and Indian region. Indeed, in the famous story Journey to the West (with the ever recognizable Wukong) the chosen route to reach India was neither through the the shorter jungle or Tibetan route, but through Xinjiang and south.

So, China is a very contained region. But this doesn't answer the question of why a united contained region? In reality, ancient China is a very sparse empire. It's power base in the Han era lies entirely in the Yellow River valley and its surroundings; and this is because of the nature of rice cultivation**. You need a river, preferably with extensive floodbanks. And you need to control the flooding with complicated water systems, or suffer famine when it floods over your dikes and ruins all the crops. After the fall of the Han and the periods of great disunion following, the base shifted to the Yangtze River which the various southern dynasties built up while the northern Yellow River continued to suffer from division and warfare. The Peral River Delta would also grow in prominence. Control of these three rivers was de facto control of the food supply of China. Furthermore, the rivers required careful central planning to be productive and avoid famine in the Middle Kingdom. It is only natural therefore that China should fall into line with whoever controls these focus points of Chinese civilization-- or face starvation and superior manpower.

If an independent nation were to form in China, it must by necessity hold one of these river valleys. The Pearl Delta however is not large enough to support a robust state that could resist the more powerful northern regions from exerting control over it's precious resource, and so fostered rebellions but not independent states (outside the Southern Ming, which one can take as a state or a rebel faction). The Yellow and Yagzhte Rivers are close by one another, and any two kingdoms formed along them are in natural opposition to eachother. The division of the Three Kingdoms and eventual Southern and Northern dynasties were based on this. It is perhaps then up to inevitability that one would conquer the other, and come to express a new hegemony over China.

Though this answer does propagate a particular view of history (And people sure do dislike anything to do with a certain book), and certainly doesn't answer to all the nuances of the Chinese history and state, I think it's good to keep in mind these realities underpinning the civilizations in China, and how they limited and shaped their ability to act. They certainly form a piece of the puzzle.

**Edit: Some quick reading shows ohea to be correct; rice was not cultivated along the Yellow River Valley!

This is actually a question I'm also very interested in and have spent quite a bit of time studying- there's still much more to learn but at this point I can identify at least a few significant factors.

Probably the most immediate cause is simple geography. The Roman Empire shared long borders with more-or-less populous regions and for that reason it was open to larger incursions, more often, whether it was from rival states like the Sassanids or from Germanic confederations or, later, from an emergent Arab empire. The Roman Empire also had a large number of geographically-dispersed, culturally-disparate population centers that could serve as regional power bases and eventually distinct kingdoms. In contrast, classical Chinese population and resources were densely concentrated in a narrow band along the Wei and Yellow Rivers, surrounded by a large, secure hinterland. The Tibetan and Yungui plateaus protected China from invasion from the west and south, there were no serious naval powers to threaten the east, and to the north there were only nomads, who could pose a military or political threat but not a demographic one due to their small numbers.

Culture is a secondary cause, and one closely related to geography. In East Asia, agriculture, literacy and the state all originated in the Chinese heartland and expanded roughly in pace with Chinese political and cultural influence (even if "Chineseness" is a very hazy concept at such an early date). The Ba culture in Sichuan developed a distinct writing system and material culture, but had the misfortune of being pinned between the Tibetan plateau and the already more-numerous Chinese states. The hilly and humid territories south of the Yangzi were underpopulated until the introduction of irrigation-intensive wet-field agriculture by Chinese settlers; Yunnan eventually produced indigenous states like Nanzhao and Dali that resisted Chinese encroachment in an organized fashion but Hunan, Guangdong, and Fujian never did. The contrast with Rome is pretty clear- Italy was a latecomer to Western civilization and Roman power was built on conquering what mostly were already prosperous urban cultures with distinct political traditions and social models. The Romans were unable to monopolize high culture the way the Chinese were able to within East Asia and I think this enabled the "idea of China" to persist through the post-Han centuries of disunion at the same time that Roman reunification was coming to be recognized as a lost cause.

Looking more narrowly at late antiquity, when Justinian failed to reunify his empire and Yang Jian (Emperor Wen of Sui) succeeded in reunifying his, you can see how a Roman reunification was a drastically more complex military feat. Northern China lacked defensible terrain or natural barriers and tended to rapidly consolidate under just one key power; that one key power was then strong enough to overwhelm the South if they could only make it across the Yangzi. Yang Jian took this Northern state (the Northern Zhou) from within and conquered the South in just a single campaign against the area immediately surrounding the Chen capitol at Jiankang (Nanjing). But to reunify the Roman Empire from Constantinople meant holding the borders against the Sassanids and Avars while launching logistically-complex seaborne expeditions against a half-dozen warlike kingdoms and suppressing heresy as they went.

There are certainly other factors, and an element of probability and random chance, but these are the ones that have stood out the most as I've been reading.

China has in fact broken up into separate nation-states like in the case of Europe multiple times throughout history. The most famous ones (many of these now part of popular culture) being the Spring and Autumn Period, the Warring States Period, and the Three Kingdoms Period. These are not periods of 'disunity'. Rather, the nations that existed during these times all considered themselves independent, separate nation-states. The Warring States period, in particular, saw the widespread use of different written and spoken languages for each state, cultural differences, and more.

What must be understood is that prior to the Qin Dynasty - as in, the Xia, Shang, and Zhou Dynasties - rulership in Ancient China was fundamentally different from the imperial system of absolute power it is now associated with. The Xia, Shang, and Zhou Dynasties were more roughly akin to a feudal system, where one 'higher' king ruled over 'lesser' kings and lords. The Qin Dynasty marked the first time in Chinese history when the imperial system of absolute power under one "Emperor" was put into practice. Although the Qin Dynasty itself did not last long, many of the government structures and practices were carried on to the next generation.

The primary difference between China and Europe, however, is a cultural power principle translated into English as "the Mandate of Heaven".

While the European nations, following the fall of the Roman Empire in the west, failed to group together as a single unified imperial entity after that, the Chinese belief in 天命 (Tian Ming), or the "Mandate of Heaven" dictates that the heavens will naturally appoint a "Son of Heaven" (the Emperor) to maintain order and stability in the land. When an Emperor is dethroned, it is interpreted as the heavens willing it, and that he has lost "the Mandate of Heaven", and thus the war and strife that follows are the heavens' way to searching for a new "Son of Heaven" to carry on the "Mandate of Heaven".

Revolving around the "Mandate of Heaven", China tends to follow a pattern of war and strife leading to the succession to the "Son of Heaven", usually the militarily-minded founding emperor of a dynasty, whose descendant emperors usher in an golden age of prosperity around the middle part of the dynasty's lifespan, and near the end of the dynasty rampant corruption and ineptitude will lead to the loss of the "Mandate of Heaven". This subsequently leads to more war and strife, and so the process repeats itself all over again.

So while China may seem 'large and unified' at multiple points in its history, at the end of every single dynasty there have been periods of massive strife and struggle. The common misconception is that each dynasty carries on peacefully to the next, when in fact, the transition period from one dynasty to the next is marked by intense conflict.

It is also somewhat difficult to explain in a single post the nuances of each and every dynasty of China, all of which had their own unique characteristics and reasons for their rise, central period golden age, and eventual downfall.

Of interesting note, however, is the collapse of most dynasties tend to follow the "Byzantine" track, in that the Emperor gradually lost his absolute central authority to outlying governors and commanders who instead of being appointed by meritocracy started passing on their powers to their descendants.

Also interesting to note is that the "Mandate of Heaven" led the Chinese people to be more accepting of foreign interlopers than most. Some argue this is because the people believed the "Mandate of Heaven" had simply passed onto these outsiders. Biggest case examples are the Mongol-led Yuan Dynasty, and the Manchu-led Qing Dynasty. In more modern times, this attitude is seen as the reason Chinese 'collaborators' tend to spring up in periods of foreign occupation, such as in the case of the Century of Humiliation by European powers in China, and the Imperial Japanese occupation of China.

Just to go off the China vs Europe discussion being held in this thread...

Is it possible that there were more cultural similarities between the different states /peoples in China than on the European continent -- which allowed for a unification of China, and not of Europe?

I'm particularly thinking of how Mongolia (not the inner province) never really became part of China, in large part because they were considered to be the barbarians -- much like Germania and lands beyond were "barbarian", or, in more realistic terms, just too different from the Mediterranean world.