I remember reading a theory that talked about that. It was about the natural theory of government evolution. I've tried to find it again since. I remember it being in response to Marx's ideas. This is my best guess recollection:
Societies develop governments to suit their needs. Tribal governments are the first. A leader rules with absolute power but with a general consensus of the governed. If his rules are bad then he will be deposed or people will leave his group to form/join other groups. As the society grows, this becomes inefficient. To obtain more stability monarchies form. The monarch rules absolutely and the people have little say in the government. This will last until a middle class starts to grow.
As the middle class grows, various forms of rights and protections are demanded. The middle class will demand a voice in government and various representive structures will be added. Eventually the middle class will choose directly or indirectly the members of government.
If this is true, attempts to install republics without a middle class will always fail. We should look to the society of a developing country first. If it has little or no middle class, we should recommend a monarch. As a middle class develops, we would encourage the monarch to nurture representative governments.