Lol you're a fucking retard.
Absolute monarchies (and other forms of autocratic government) can ensure stability for a while. However, their fundamental problem is that they end up promoting technological and economic stagnation, because power is concentrated in a small group of elites that fear creative destruction.
Technological changes threaten the power of the elites. See the industrial revolution, where autocratic monarchist states (such as Russia, Austria, and Qing China) were suspicious of new technologies such as railroads, because they threatened the feudal system that the elite derived their power from. Railroads come in, that means peasants can leave and new ideas can come in, which makes the population harder to control and extract wealth from.
The same dynamic plays out with economic change. Changes in economic conditions (such as industrialization) mean that people other than the elites can generate wealth, and become potential threats to power. A new class of increasingly wealthy entrepreneurs is a threat to the elites.
Together, these factors mean that an autocratic absolute monarchy has very little reason to promote economic or technological growth, in the name of stability. The problem with that is that it eventually dooms the nation to conquest or exploitation from without, and internal upheaval from within. Which makes the very premise of absolute monarchy (stability) irrelevant.
Of course, you could have an intelligent monarch who realizes this and works to promote development within his nation. The problem here is that monarchs are people, and people are mortal. What prevents a total retard whose in the line of succession (such as Wilhelm II or Nicholas II) from getting into power when the competent guy kicks the bucket?
Absolutism is a dead gay ideology, along with communism, multicultural democracy, and fascism.