I can easily recall a number of major finds from the 1800s through the 1940s. For instance: The Dead Sea Scrolls (first discovered 1946), The Nag Hammadi texts (1945), the Chu Silk Manuscript (1930s), The Liber Linteus (discovered 1849, identified as Etruscan in 1891), The Oxyrhynchus Papyri (1896), the Dunhuang Manuscripts (1900), etc.
But curiously I’m having trouble of thinking of any major ancient manuscripts that were discovered since then. Am I just misinformed about this, or has there been a decrease in the number of discoveries? I would have assumed that there would be vastly more discoveries made because of modern technology and archaeology techniques.
Although new papyri still turn up every year, there has indeed been a slowdown in the pace of discovery. Without focusing on a single region, there are several basic reasons. Most of the great discoveries were made during the heyday of the colonial empires, when the major European powers had the might and political will to send expeditions and wandering scholars to far-flung corners of the globe. Since this period coincided with the first flush of globalization (but came before a global antiquities market or national restrictions on the export of antiquities), it was still possible to find isolated monasteries and troves of papyri that only locals knew about. As a result, a few decades of expeditions snatched up huge numbers of texts.
To focus more specifically on Egypt, the great rush of papyrus discoveries (above all at Oxyrhynchus) coincided with a major push of farming and settlement into regions that had been largely depopulated since antiquity. Farmers digging for sebakh (the decayed remains of mudbrick, useful as a fertilizer) began uncovering papyri that had been undisturbed for two millennia. As soon as farmers realized that foreign dealers were interested in the papyri, massive treasure hunts (followed by a series of formal excavations) revealed the vast majority of the papyri now known to us. Not all, of course, were uncovered; but the continued growth of Egypt's population (which has driven the cultivation / saturation of new lands) and the construction of the Aswan High Dam (which has raised the water table throughout much of the Nile Valley) both conspire against the survival of unexcavated papyri.