It's demonstrable from many datasets that the rich get richer and the poor get poorer. Look at FRED mobility data. Look at Forbes 400 richest. Look at what percent of the richest x% are first generation. Look at FRED data on intergenerational wealth.There are ample datasets showing that wealth regresses to the mean.

Pick a definition of wealth (income, or ownership, or whatever), and pick a dataset for which you can capture all in that bracket for some reasonable timeframe, and for which you can see what percent moves out. For every such dataset I've found over years of looking at this, every one backs the claim that the rich do not stay rich.

Most rich people are newly rich. Most rich families drop year over year in total wealth.