The answer is yes because you being wealthy does not mean that your finance can't decline, it very important for everyone to save wether you are reach or poor, that's why the rich is always in search of lucrative investment because of the fear of being poor, the rich look for more money by investing in different things in other to keep their wealth by so doing they are practicing savings in disguise.
There are also instances where those rich people are like addicts to earning money, meaning they want to earn more. As you know, if you are earning a lot, you will now want more, and being rich means you need a lot of things to be paid for, so if you don't find another source of income or your earning keeps slowly declining, then that is a huge problem. Also, regarding saving, if you are rich, you can now easily save as you do have a ton of spare money.