Goethe wrote a terrific paper on plant reproduction. In it, he describes how reproduction in plants occurs after a systematic buildup of the resources which enable it.
One of the classic ideas in Western civilization is that the Roman Empire fell to savage tribes of Goths in what is now Germany. The problem with this idea is that the Empire bifurcated about 100 years prior to that, in a process quite similar to the process Goethe identified in plants. The Western half of the Empire remained headquartered in Rome, the Empire's origin, and retained the original name as well. But the other half had its headquarters in Byzantium (aka Istanbul, aka Constantinople), and began to be called the Byzantine Empire. Although the Roman Empire's Western half collapsed only about a hundred years later, the Eastern half persisted for an additional thousand years, until sometime between 1450 and 1480 (depending who you ask).
Even that longevity looks paltry compared to my preferred interpretation, however. Assume for the sake of argument that empires exist primarily to establish hereditary advantages for the members of particular classes of people. Or, alternatively, that there is, at the core of any empire, a system which exists primarily to establish hereditary advantages for the members of that empire's aristocracy.
Depending on which variant you prefer, you could say that the aristocracy-favoring system within the Roman Empire abandoned the Empire and took over the Roman Catholic Church instead, or that the Roman Empire abandoned many of its governmental aspects and became the Roman Catholic Church. Keep in mind that popes commanded armies and exerted governmental authority in and around Rome for well over a thousand years, all the way up to 1870. Even today, the Church may be the third-biggest landowner in the world, although its vast wealth is difficult to calculate from the outside. And I had a Latin teacher in high school who met a Catholic priest from Poland and had a conversation with him in Latin, even though my teacher spoke no Polish and the priest spoke no English.
Consider also the British Empire. The best estimate for the official fall of the British Empire would be 1997, when control of Hong Kong reverted to mainland China. Likewise, although Britain lost its American colonies as early as the 1700s, colonies like India, Pakistan, Palestine (now Israel), and many others remained under British control until the middle of the 20th century. Although Canada became semi-independent in 1867, and Australia in 1901, Canada didn't officially finalize its separation until 1982, and Australia did it in 1986.
Here in the States, we tend to underestimate the British Empire's lifespan, because we got out of it much earlier than average. But again, there's an alternative interpretation which attributes even greater longevity to that empire as well. As with Rome and Byzantium, the Empire bifurcated, and its older half shriveled to a non-imperial status, while its newer half - the United States - continued to thrive as an imperial power right up to today.
The exact degree to which American foreign policy is imperialistic or democratic is wildly contested, yet its near-total domination of global politics is pretty hard to dispute. And again, just as the Roman Catholic Church kept some core elements of the Roman Empire intact, while allowing many others to atrophy, the US is quasi-imperialistic where the British Empire was unequivocally imperialistic. Both subsequent pseudo-empires have kept the original empire's language alive, as well as continuing to privilege the respective aristocracies involved, while dropping many of the core governmental and militaristic aspects of a true empire.
I can't prove this, but I believe that if you follow the money in either case, you'll find continuity. In the Roman example, my guess is families and companies which began in Rome were able to persist either through the Byzantine Empire or the Roman Catholic Church. In the British example, my guess is families and companies which began in England or Scotland were able to persist through the American continuation of British law, or through international corporations (which were originally invented by the British for explicitly imperialist purposes).
Whether this represents genuine imperial persistence or a vaguer kind of imperial drift is an interesting question, but not one I'm qualified to answer. It could be that empires are caterpillars, and their butterfly forms are more loosely organized and less explicitly governmental. But the continuity's easy to spot in either case, and I definitely think the commonality here is real.
Since pretty much everyone who reads my blog is a programmer, I'll bring this around to tech.
In the 1990s, I and many others assumed that Microsoft would die out because of the Internet. I'm sure a big crowd, twenty years before that, thought Microsoft would kill off IBM forever, too. Both these companies have been considered "empires" in their day, though never in a purely literal interpretation, of course. Each of these companies currently survives in a form which is very different from the form they held during their respective imperial glory years.
It's possible that this is always how it's going to be, and that Google will still be with us, in some radically mutated form, two hundred years from now. Likewise, if you're a tabletop gaming nerd, I used to think the Roman themes in Warhammer 40K were ridiculous, but those mecha legionnaires look more realistic to me these days.