The Dead Sea Scrolls seem to be a once-in-a-century find, but I keep thinking about the vastness of the deserts and how many settlements, structures, and tombs might have vanished beneath shifting sands.
This is a question for archaeologists, not historians, except insofar as the historical record tells us that there were once _lots_ of written materials.
In fact, preserved papyri are found quite often -- your impression of "once in a century" is off by a lot. What made the Dead Sea Scrolls so unusual was their content; much of what gets found is quite ordinary, material known from other texts.
And even then, there are still extraordinary discoveries. In the past decade, Pierre Tallet and his team have been retrieving some of the oldest papyri yet found, including the celebrated "Diary of Merer" from roughly 4,500 years ago (eg 2500 years _older_ than the Dead Sea Scrolls); found at Wadi al-Jarf in Egypt.
There's every reason to believe that there are more papyri waiting to be found. And of course, in ancient Mesopotamia, clay tablets were often used-- these are extraordinarily durable -- we've already found on the order of a million of these. It's pretty much a certainty that there are many more to be found. Even without finding another tablet-- only perhaps 100,000 of the million odd tablets have been read in the modern era; there are potential blockbuster discoveries waiting to be found by assyriologists "digging" in the bowels of the British or Iraq National museums.
See:
Pierre Tallet, and Gregory Marouard. “THE HARBOR OF KHUFU on the Red Sea Coast at Wadi Al-Jarf, Egypt.” Near Eastern Archaeology, vol. 77, no. 1, 2014, pp. 4–14.
[open source-- describes the discovery and has photographs of the remarkably well preserved papyri-- demonstrating that in a hot dry climate and shade, papyri can last a very, very long tim]
https://www.newyorker.com/culture/culture-desk/a-new-history-of-arabia-written-in-stone
You might interested in this article. They aren't "scrolls", but new 2000-ish year old Safaitic inscriptions are turning up pretty much every time Ahmad al-Jallad has the chance to go on a new expedition. You can also follow him on twitter here: https://twitter.com/safaitic?lang=en
To add to the posts above, there are quite a few ancient archives mentioned in published texts but have not yet been found. This is primarily because many important cities have not yet been located, such as Agade (capital of the Akkadian empire), Ekallatum (one of the capitals of the kingdom of Upper Mesopotamia), Waššukanni (capital of the kingdom of Mitanni), Tarḫuntašša (briefly capital of the Hittite empire), and Kummani (the capital of the kingdom of Kizzuwatna).
In other cases, we have identified and partially excavated ancient cities but have not yet found their archives. For example, there are no doubt dozens if not hundreds of cuneiform tablets buried at Qantir (ancient Per-Ramesses) in Egypt, but so far only a tiny fragment of one tablet has been found.
As u/amp1212 mentioned, there are many texts that have been excavated but not published. I wrote about these in Are there any ancient texts that have yet to be translated due to a lack of translators?
