Has any power managed to rule for more than a few hundred years?

I'd say Mesopotamia, Egypt, Ancient Rome, Holy Roman Empire.

Several Chinese dynasties depending on where one draws the line on "a few"

rome?

I guess if I'm a dictator worried about my legacy, I'd be okay with being remembered as "not quite as successful as Rome"

Especially if you include the Eastern Roman Empire which fell in 1453.

That's a bit of a broad generalization. As with all history it doesn't hold up under scrutiny.

In the 1200s, the empire split into 3 warring countries. The one that took Constantinople was considered the continuation of the Byzantine empire, but maybe it's more correct to think of it as a spiritual successor, than an actual unbroken reign of a single nation.

Which would put it at less than 1000 years of rule. So "a few hundred years" would still be an accurate upper bound.

Even if you take the 1200's as the end of the Empire, and ignore the Roman Republic and take 31 BC as the defacto start of rule of the Roman Emperor, you still are looking at over a millenia.