In certain industries there are mandatory retirement ages, but for those that are in the highest echelons in politics, whether as a dictator or a monarch, they are almost never subject to mandatory retirement ages, and a surprising amount of those in office, will not voluntarily relinquish their office, even at very advanced ages, or when in obvious ill health. The closest semblance of an American President taking on the mantle for life was Franklin Delano Roosevelt, who was elected four times to the highest office of the land, before dying in office. Since the passage of 22nd Amendment which limits the term of a President to two terms, Americans will no longer be subject to possibly having a President that will essentially be a President for life, though it has had members of Congress, serve terms of 57 years.
In today's world, Queen Elizabeth II of England has been the Queen for 65 years, and became 92 years old in 2018. So too, the Sultan of Kedah, and supreme head of state of Malaysia, died in office at age 90, after serving 59 years; as well as King Bhumibol Adulyadej of Thailand, died in office at age 88, after serving 70 years. Dictators such as Fidel Castro, who ruled 52 years, left the office before his death, only because he could pass the office onto his own brother. Kim Il-sung ran North Korea until his death for 48 years, and Chiang Kai-shek, ran the Republic of China, also known as Taiwan, for 48 years, until his death. The list of monarchs and dictators that served in office for incredible long terms is quite extensive, demonstrating that those that are placed into power, and cannot be democratically overturn from that power, often do not give it up, until their physical death.
The most plausible reason why those that are very old, and are often suffering from physical bodies and minds that are in noticeable decline, yet still are clinging onto their power and position, is certainly not because they are needed by the fellow countrymen, and definitely not because they are irreplaceable, although both of these reasons are touted as being correct; but rather that the power behind the throne, the power that is often unseen, unknown, and disguised, has a vested interest in the dictator or monarch continuing in power, as long as they shall live, because their power depends upon the status quo, and they do not wish to risk their position with a changing of the guard.
The fact of the matter is, to run any country, especially a nation that consists of millions upon millions of people, with different religions, different factions, a mixture of private and public enterprises, domestic insurrection, wars, famine, infrastructure, modernity, the internet, and so on and so forth, is a task that necessitates a strong team of individuals for advisement, logistics, and throughput, of which, no dictator and no monarch, even at their peak of their health and mental powers, could possibly keep their hand upon the wheel for everything that is happening. This does mean that dictators and monarchs are absolutely dependent upon the people and personnel that ostensibly report to them, and they are at the mercy of those seemingly endless reports, of which, the manipulation of a dictator or monarch that is on the wane, is child's play for those that wield the power behind the power.