I think rich kids will often lack the inner motivation and discipline to see a startup through. That's the flip side of knowing you can fail and it won't impact your life negatively. Startups are really hard, if you don't have that burning desire and fear of failure driving you forward, I don't think too much of your chances.
Anyone rich, or not can try again and again, it will just be harder for people who also need to figure out how to pay the bills.