What does your 'research' consist of? Reading anti-Semitic conspiracy theories online?

As far as established history goes the Rothschild family is not unique in the slightest; other than being uniquely targeted by said conspiracy theories. Your question seems premised on a conspiratorial outlook as well, since it's pretty non-obvious otherwise how a very large family that's existed for centuries in different countries could just be assumed to all act in concert.

You state as if it were fact that other families "never manage to stay afloat for much time at all" yet what is this based on? It runs contrary to most research in economic history that shows on the contrary that families most often do retain wealth across centuries. Clark's seminal research showed that (counter to expectations) even in a non-feudal society with high social mobility in the 20th century, most families who were wealthy nobility 200-250 years ago are still wealthy now. Research confirmed by other studies such as those by Bengtsson et al. Barone and Mocetti's went even farther back in Florence, Italy and showed that many of the town's richest as far back as the 15th century remain at the top.

It's not one of the 'biggest problems when it comes to history', on the contrary it is the rule and not the exception that families hold on to their economic status, at least in comparison to the general population.

But that's show conspiracy theories work. They dazzle people who don't know better with supposed 'oddities' that aren't odd at all, and the people who are wont to believe don't go about challenging whether those oddities are actual oddities in the first place. So "isn't it strange that they've held onto their wealth so long?" No, it's not. It's not a great mystery of history. It's in fact what happened in more cases than not for most wealthy families. So rather than ask historians to justify this flawed and incorrect premise, maybe you should direct your research into where your premises are coming from. Since it didn't come from some open-ended examination of wealth inheritance, where did this singling out of the Rothschilds come from?

Recommended reading:

Gregory Clark et al, The Son Also Rises: Surnames and the History of Social Mobility, The Princeton Economic History of the Western World Book 49, Princeton University Press, 2014

Bengtsson, E., Missiaia, A., Olsson, M., & Svensson, P. (2017). The Wealth of the Richest: Inequality and the Nobility in Sweden, 1750–1900. (Lund Papers in Economic History: General Issues; No. 161). Lund: Department of Economic History, 2017

Thomas Piketty, On the Long-Run Evolution of Inheritance: France 1820-2050, Paris School of Economics, 2011

Guglielmo Barone and Sauro Mocetti, Intergenerational Mobility in the Very Long Run: Florence 1427-2011 , Bank of Italy Temi di Discussione (Working Paper) No. 1060, 2016