1 Happiness is all about meeting the needs
Happiness is all about meeting all of our important needs. A person might have a need to be rich and another one to be healthy. If the first need was met while the other was not than this person won't feel that happy. If both needs were met together this person will be very happy.
2 Some people don't care much about money
Some people have many important needs that don't include getting rich. The need to be free, to travel around the world, to be popular or to live in peace can be more important than the need to be rich. If a rich person doesn't care much about money then money might not make him happy.
3 They compare themselves to richer people
A millionaire can still feel really bad if his cousin or friend is richer than him. While some people don't care much about comparisons of wealth others always think about them, and as a result, might feel really bad even if they are rich.
4 They want to get more things
A rich person might have a Ferrari but he still might be unhappy because he doesn't have a private jet or a large mansion. Rich people can feel less rich if some of the things they badly want to buy are out of their reach.
5 They live very stressful lives
Some jobs are extremely demanding. A person who feels very stressed because of his job might wish to have less money in exchange for finding a better job. If each day is full of short term pain then life can be very unpleasant even for a very rich person. (See The body language signs of stress)
6 Fear of losing wealth or status
Some rich people can live in fear especially if the risk of losing wealth or status is present. Business men who go through very risky projects might feel unhappy because of the fear and anxiety they have to go through.
7 They still feel financially insecure
Many rich men still feel financially insecure and believe that they don't have enough money. As a result, they don't feel happy with their wealth and might even feel miserable. (See Why are some rich people stingy?)
8 They have other serious problems
A rich man can have his financial problems solved but he might have some other serious problems that money can't solve such as a serious health issue.
9 They compare themselves to very competitive people
Rich people always keep an eye on other rich people. This very competitive environment can prevent a person from enjoying what he has and can make him unhappy.
10 Inherited money can make a person feel worthless
Some of the rich people who inherited their money might believe that they are worthless as a result of believing that they achieved nothing in life. They know that their money was made by someone else and that's why they might feel unhappy until they prove their worth.