What pushes the wealthy to want to become wealthier is determination to stay on top, they understand that wealth can vanish if it's not sustainable. I believe that wealthy people have phobia for poverty, they are afraid to become poor like the those that comes to them for help. This is the reason why most financially wealthy people will do almost anything to become more wealthy because it is better to go from grace to grace than descending from grace to grass. Everybody wants the good life and those that have it knows that if they relax they might not be able to compete with other wealthy people.
I think the determination is when you have already made it. There are people with determination to want to be wealthy in their life but they don't have the means to start. To build wealth, you have to build a very standard foundation for your life, you have to build what will make you go far and the right connection because without connection, you can't make stay wealthy for long time. Any wealthy person you can think of has some network and connection.
It's after you have built your foundation the determination to be at the top will come in, that's when you should be thinking how to remain at the top forever and how to make sure you never make some of the mistakes you made while building that wealth.