I've been reading up on Rome from the start of the empire to the Severan dynasty, and it's surprising to me that the empire had so much trouble keeping a dynastic family on the line. As far as I know, there wasn't a biological dynasty that lasted longer than three members; while the Antonine dynasty went through 6 members, all heirs were adopted, not biological.
So why did Rome have so much trouble? China had no issue keeping dynasties for several hundred years before and during Rome's time. After the empire fell, its successor countries like France and Austria also maintained long lasting dynasties. What was the difference?
It has to do with the way the Romans interpreted families and inheritance. u/mp96 gave a comprensive answer to a similar question here. It might interest you that our concept of inheritance and absolutism is a construct that had not yet emerged in the Roman empire:
During the late Roman and Merovingian/Carolingian world, land ownership and political power was quite widespread, as partible inheritance was much more beneficial for the purposes of spreading out your familial network and influence. The more spread out your family's power, the more assets you could call on.
While,
On three occassions during a period of ~140 years, a practise was about to be set with succeeding biological children. All three of them failed because the heirs were nowhere near as competent as their fathers.
One thing to consider is that the position of Emperor in ancient Rome wasn't a monarchy like you'd see in later European or Eastern empires. When Augustus became the "first Emperor" he wrapped himself up in the trappings of the Roman republic. Augustus' legal powers gave the appearance of making him just another Republican magistrate. The title Augustus went by too, didn't have Imperial or monarchic pretensions Princeps, or "First Citizen."
Additionally Augustus' legal powers were granted to him by the Roman senate, they weren't something he could bequeath to an heir. for this reason Tiberius, who would finally succeed Augustus, was granted all the powers that Augustus held before Augustus' death. Tiberius succeeded Augustus not because he had adopted Tiberius as his son, but because Tiberius was legally emperor all ready. So the succession of Roman Imperial powers are tied up in the facade of Republican ettiquette. Julius Caesar was famously assassinated for trying to make himself King, at least to the senatorial elites, openly designating an heir and promoting dynastic interests would have been a clear signal to the elites that you had some despotic eastern monarchy in your head and needed getting rid of.