Except, Armored Diplomacy, aren't you're forgetting the big problem - how to make them last long in the first place to get today's tech? It's not space bat, but definitely WAY HARD - remember, the OTL Romans failed, though they had a pretty amazing run.
Even if it survived continuously, my guess it probably would've through at least one more revolutions and likely be Commie or Iranian-style theocracy, but Christian, or as fake democratic as Russia under Putin. Remember, China, a similarly long-laster, has hardly kept its same government, has it? Nor Japan. No more than Rome OTL did.
And, remember, it's hardly likely to have anything like Rome's height of turf. And it's likelier to be around Asia Minor (Turkey) and Istanbul than Rome, because that was more strategic - that's the Eastern so-called Byzantines lasted FAR longer than the Western Romans.