I think it can be helpful to think in terms of the ways in which the "turnover" of historical ideas varies in different periods and genres of history.

Generally speaking, I would say that when it comes to what might roughly be considered the modern period, say from the French revolution to whenever you think that "history" now morphs into current affairs, it's rare for even the most significant works to remain unsuperceded for any longer than about 20 years. For the early modern period, the same "turnover" of ideas takes longer (except perhaps in a few of the busiest and most contentious areas, such as the English Civil War/Revolution/War of the Three Kingdoms – the changing terminology is itself a clue to the intellectual ferment going on.) Then when it comes to the period from antiquity up to the end of the Middle Ages, the turnover time is longer again. This thread amusingly illustrates the ways in which classicists and medievalists still read, cite, revere and – perhaps most importantly – think about and use, works written, in some cases, as long as 150-200 years ago.

Why these differences? One key factor is the availability of sources. The sheer quantity of material available for the modern period is so vast that no one historian can read and master all of it; far more, and far more significant, variant opinions can emerge from such huge masses of evidence. In the very modern period, of course, huge tranches of completely new evidence can emerge, forcing a rewriting of everything that has gone before. The opening of Eastern Bloc archives in the 1990s is perhaps the best recent example; it led, tellingly, to the well known Cold War expert John Lewis Gaddis effectively setting aside a lifetime's scholarship to write a book entitled We Now Know.

In contrast, it's quite rare for entirely new sources, written ones at least, to emerge from older periods. If you are an Anglo-Saxonist, you may well be challenged and excited by modern archaeological finds and new interpretations of old archaeological evidence. But you are still going to be reading almost exactly the same written sources as Frank Stenton was reading in the 1930s and 1940s, or even Bishop Stubbs 70 years earlier again. And while the specialists in this period do try mightily, there's a limit to how much reinterpretation one can place on many of the Anglo-Saxon Chronicle's earlier one line entries.

I'm exaggerating a little for effect. Scholars of the most obscure and little-evidenced times and places are capable of truly exciting and innovative (and convincing) work - I'm thinking here of the likes of Alex Woolf's work on the Pictish kingdoms. But I remember clearly that when I was choosing which periods to study as an undergraduate, one of the main attractions of opting to study Saxon history rather than say the Civil War period, for a mandatory British history course, was that I had a much better chance of being on something approaching a level playing field with my supervisors just in terms of having read the same stuff than I could possibly hope for if I chose a later period.

Broadly, then, the answer to your question is going to be that the older writers who endure longest will tend to be those working in the most distant periods. And I'd add that the ones most likely not to endure are the writers of grand, over-arching theories of everything, like Toynbee, or Jared Diamond. That's because their work is going to be based on hundreds or thousands of not-fantastically-well-informed takes on many, many different times and places and historical currents - in each of which scholarship is constantly pressing forwards, at varying paces, yes, but in ways no one grand theorist can possibly hope to anticipate or keep pace with.

Where have you heard that Carlyle's work on the French Revolution "still holds up"?

I mean it is an enjoyable read, like Gibbons Decline and Fall of the Roman Empire it can still be read as a literary classic, and it played an important role in English historiography on the subject, and it is within these fields that it is still studied, but it would not hold up in any way if you wanted to learn about contemporary scholarship on the French Revolution.