Well, consider my example in https://news.ycombinator.com/item?id=29286002 of al-Azhar University, which is 1050 years old. It was founded under the Fatimid Caliphate, which fell 200 years later after a century of civil war, replaced locally by Saladin's Ayyubid Sultanate. Another 80 years later Cairo fell to the Mamluk Sultanate, which held Egypt for 270 years until the Ottoman conquest, which the Ottomans lost 350 years later to Napoleon. Five more governments later (if we count Nasser, Mubarak, Morsi, and Sisi as a single government), here we are, and al-Azhar has survived the fall of nine governments, all of which entirely ceased to exist. This suggests two points:

1. There are a lot more small organizations at any given time than large ones. There were only two Caliphates at the time of the Fatimid Caliphate (the other being the Sunni Abbasid Caliphate, to which we owe Western Civilization, such as it is), and they covered the entire Middle East. But at the same time and in the same place there were thousands of schools and universities, some of which did get blown up by catastrophes (like the House of Wisdom in Baghdad) and some of which did not.

2. There are a lot of catastrophes that are harder for a big organization like the Fatimid Caliphate to absorb than for a smaller organization like al-Azhar University. More generally there are certain kinds of organizations, such as universities, that are very resilient.