Challenges faced by non-democratic governments?

The challenge that their population will begin to reject the concept that their leaders have the "divine right" or moral authority - or whatever - to continue to determine the direction of their government. Increasing degrees of force would have to be made to insure those in power remain. "Consent of the governed" is a major factor in the democratic system. Tyranny of the majority then becomes the problem unless rights of the minority are preserved (i.e. U S Constitution and Bill of Rights).