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.
Aren't we all scared to lose money or be poor? Life is difficult and if we do not maintain what we have or aim for higher, we will surely feel the challenges of not having money.
When you are or have experienced the more luxurious part of life, it is hard to go back to being poor that is why wealthy people would really want to aim for staying rich or even richer.