I watched an interesting interview with a billionaire a while ago, who said that after you reach a given net worth it actually becomes very hard (unless you're unlucky) to significantly diminish your wealth through consumption, and that in fact consuming more goods often just increases your net worth: Luxury cars, apartments, mansions, real estate, parks, yachts or resources like gold often appreciate in value with time (at least they did for the last 60 years), so the more of your money you spend on these goods, the richer you'll become. The words that the interviewee used were "if you're rich you can't destroy money by consumption", which is of course not 100 % true, but explains really well why the rich are getting richer.

In addition, many countries have much lower taxes on capital gains compared to other types of income, which is another factor that favors further concentration of money with those people that already have a lot of money.