The main issue is geography : Mediterranean basin tend to be both undercut by geographical obstacles (Alps, Balkans, etc.), while in the same time, Romania had several strategical weaknesses at its borders as Illyricum and Oriens. China was more or less the contrary : it had few geographical obstacles within its core areas, and fairly distinguishable geographical borders.
While Sahara played something akin to Gobi for Romans, most of the raiders and Barbarians of the Late Empire didn't came from Africa.
As much as China went trough periods of desintegration, the core areas were still ties by a clear geographical, cultural and economical continuum. Rome? Not so much and the continuity was harder to maintain on a political scale.
Now,
@The Undead Martyr mentioned the Arab conquests as a rupture in the continuity of Late Antiquity, but I don't think it would be really accurate to say it was the cause of the rupture.
Most of the links between Eastern and Western Romania weakened in the late VIIth century, and especially after Mauricius' reign, as the Romano-Persian wars really limited the Byzantine trade (and more critically coinage) in the West (whom Late Ancient trade was already diminished, but not disappearing, from the collapse of the western Roman state) in the same time new trade centers appeared on North Sea.
Even there, according Richard Hodges, the long-range trade in western Europe remained largely on the same grounds than before the Arab conquests, and was actually maintained trough trade with Arabs (Carolingian coinage is really indexed on Arabo-Andalusian's) with whom Franks were both trade partners (especially with the political unification of most of former western Romania and part of the North Sea coast) and competitors : the changes of the IXth/Xth centuries (Carolingian decline* and the political-economical reshuffle not only in the mainland but elsewhere; and the Abbassid and Umayyad own political-economical crisis) really achieved a rupture in Late Ancient world that was looming since the late VIIth century.
Then, how to maintain a longer Mediterranean cultural/political continuity?
My guess would be no Justinian reconquest (which would probably ask for Athalaric survival among other PoDs) : the responsabillity of these into the growing irrelevance of Italy and Africa shouldn't be overestimated as the plague, an unexpected and unprevisible event, really prevented any middle term reconstruction.
Still, these conquests were a pivotal change that while not irremedible, was one of the main differenciation between the west and the east of Late Romania (the three others afterwards being monothelism and Romano-Persian wars followed by Roman-Arab wars), and prevented smoother connection with an Africa** and Italy that still largely participated to a late imperial civilization (more so than in most of Gaul and Spain) akin to what existed in eastern Romania from one hand, and with the real huge cost of what ammounted to half-assed campaigns which had little preparation (Constantinople's vision of Africa was based on a fantasized provincialisation that ignored the realties of Berber/Roman dynamics since the IIIrd century, which led to a never-ending guerrilla for decades; and I won't mention the obvious cost of Gothic Wars).
Eventually, I wonder how much the absence of Justinian conquests wouldn't lead to Constantinople establishing some form of "Christian Commonwealth" political concept ITTL, seeing the various Barbarian kingdoms as auxiliaries (if independent and troublesome) into the management of Romania (in its largest sense) with Roman elite in the West, or rather what remains of the elite identifying itself as Roman (mostly in Provence and Aquitaine for what matters Gaul) as an intermediary between royal and imperial courts (as Mauricius seem to have attempted IOTL), and with the Vth and VIIth century diplomacy consisting to support Nicean kingdoms against Homeans kingdoms as rear alliance, while still acknowledging the latters as legitimate powers (especially as willy-nilly, they would end up rescind it in the middle term).
"
Of course you're legitimate kings and rulers of your peoples and kingdoms. We Romans would never dream of warring as long indirect intervention isn't involved against our valued allies and friends in [insert region].
Why, we certainly don't want to break such a good relationship we have, you being trusted auxiliiary of God's church in the west and protector of the law : it's why we benevolently give you silk, gold and whatnot whom the absence would incidentally make your hegemony over your own nobility significantly harder by the way"
Now, how long would it last is anybody's guess, altough I don't see it being maintained with the pretty much unavoidable development of Atlantic and North Sea ensemble (altough a road from Baltics to Mediterranean could pass trough the Amber Road rather than trough Russia ITTL), but it could be a first base for a complex dynastic/geopolitical ensemble that would maintain more of the political, institutional and cultural continuity in an aformentioned not that obvious geographical situation.
*Altough the political-institutional rupture with Late Antiquity more or less predates the Carolingian decline, and is partially due to Peppinid/Carolingian takeover)
**The maintain of the Vandal Kingdom was quite unlikely, but not the establishment of a strongly romanized Mauretanian kingdom over Africa, which would have happened at short term.