It's a real concern. The short answer is that we're stuck with them until they either a. resign (unlikely) b. die (natural causes, dagger in the back) or c. are overthrown (undesirable; permanent solution to a temporary problem).

In my opinion, this is the greatest downside of monarchy, but I believe it is outweighed by the positives. I also feel it is necessary to point out that under democracy, the only people who hold positions of high political power are those who actively seek power and labor to retain it -- psychologically, those who are most likely to become corrupt. The nature of democracy usually forces all politicians to make impossible campaign promises in order to obtain power; in many countries, politicians also have to seek out financial support to obtain power -- this is a massive conflict of interest between their debts to their contributors V. their duty to serve their people. Because a King is trained from birth and has his power bestowed upon him rather than won, he is generally more experienced and educated than democratically elected leaders, but more importantly, he is able to stand above partisan politics and focus on the long-term wellness of his nation -- the nation is his and so he has an incentive to maintain it, whereas a democratic leader has only an incentive to win his next election, even if it means sacrificing the long-term wellness of the nation for short-term sanctification and temporary popularity. It is a certainty that many Kings are poor rulers, but monarchy offers a better chance that a decent and well-meaning person will occupy the highest position of leadership than democracy. The trade off is that, while poor rulers will perhaps exercise power longer than we'd like under monarchical rule, excellent rulers will also exercise power until their death, bringing their nation a great deal stability & unity.