With sufficient amounts of wealth I think a royal family can easily hold onto power, with enough money you can buy off any opposition and pay for ample security for yourself, I think the driving factor behind these families remaining in power is because they of their vast amounts of wealth.
I do think the royal families in the Middle East have been able to hold their power because of their wealth. Of course, with this power comes a lot of fear and there is much fear in this region of the world. To keep the fear, they must continue being wealthy.
I refuse to believe that a person should be in power either because of their wealth or because of the fear of their population. The only legitimate one is one that is chosen by the population of consenting adults. It is a sham for a person's money or power to buy them power.
Yes, wealth tends to give a person feelings of great power and to a certain extent, it does. However, instilling fear in a nation's people, especially fear of death or of losing family members, gives even greater power to rulers than wealth alone. Using fear as a tool to rule the masses seems to be quite common in some areas.
I believe that religion plays a great role in this. It is because of the fear and power that religion has over them that the rulers can keep their hold on them. It is through this that they can create their wealth. It is not the wealth that is keeping their power but it is a result from it.