My personal favorite theory is that, much like the Roman Empire, you have a dynamic between the local aristocracy and the state bureaucracy that made it more profitable for the former to join the latter, rather than vice versa. A state is able to use its economies of scale to not only extract greater resources from the populace but also to use those greater resources to produce means of legitimacy for itself that the aristocracy can then fight over.

There was a great analysis by Max Gluckman which pointed out that the Zulu state by any stretch of the imagination SHOULD have fragmented, given the problems of communication, distance, and the relatively low level of wealth extraction when compared to early modern states. However, the ideological "wealth" of supreme leadership of the Zulu nation was powerful enough that civil wars fought amongst potential leadership claimants were for the ultimate control of the whole system, rather than localized control of their region. Thus civil war in fact reinforced the legitimacy of the entire nation, rather than factured it.

It's the flipping point of that see-saw when the state bureaucracy is unable to produce either material or ideological wealth in excess of what an individual region and its local aristocracy that can take advantage of, that, IMO, decisively favors a large state's fragmentation over its cohesion. You see this in the case the late Roman Empire, as well as the late Han Empire. For the Roman Empire, it's most notable in the breakdown of the western economy following the Vandal capture of Carthage, for Han China it was the rising power of local lords in the aftermath of the Yellow Turban rebellion, as well as the self-sacking of the capital of Luoyang by Dong Zhuo. To move the analogy further forward, the fall of the Tang Dynasty had similar problems of local vs. state power competition in the aftermath of the catastrophic An Lushan rebellion, which forced the state to rely upon local warlords for defense, warlords the state ceased being able to control.

Although with that said, I really don't think the process is inevitable. There are always individual political actors (as well as environmental circumstances) that can reverse the situation in both ways, for the good and for the bad. Merovingian Gaul was headed toward fragmentation in the early 8th century until Charles Martel forcibly reimposed his power onto southern Gaul. But then again, state could always end up with someone like Commodus, taking a fully functioning state, and running it straight into the ground.

tl;dr - Whether a large state stays together or breaks apart is dependent upon where at any moment the see-saw lies between the power of the local vs. the "federal." If one is able to provide greater opportunities and wealth for the aristocracy than the other, that is the way the see saw tips, and though trends can be reversed by individuals, it is more rare and usually at great cost.

It's not really correct to say that Chinese empires did not fracture, because they certainly did.

While not a "historical" source by any means, the opening line of "Romance of the Three Kingdoms" states that nations tend to unify after long periods of division, and tend to divide after long periods of unity.

The novel was written by Luo Guanzhong in the Ming dynasty about events that happened at the end of the Han dynasty. In between had been the Jin, Northern and Southern Dynasties, Sui, Tang, Song, and Yuan. The last of which being overthrown in Luo Guanzhong's own lifetime. Each Dynasty had succumbed to civil war or foreign invaders, who then imposed their own dynasty and were eventually deposed in through through civil war or invasions. The axiom about the balance of unity and division was true through all the aformentioned dynasties and the ones to come.

It would be more accurate to say that the rulers of China were always culturally Chinese, and if not, Sinofied relatively quickly. Continuity of government between the Chinese Dynasties was relatively low compared to say, dynasties of the Roman empire, as the decades of upheaval before a dynasty's fall would destroy much of the government institutions. Or more correctly the gross incompetence of government institutions caused the social upheavals that would destroy them, and the new rulers would have to rebuild those institutions from scratch.

Looking at the OP question from the Chinese perspective, one might ask why the Roman Empire failed to Romanize their invaders and eventual conquerors.