This seems closer to the mandate of heaven[0] than an explanation of how governments work or why they are overthrown.
Here's another explanation based on The Dictator's Handbook: Why Bad Behavior is Almost Always Good Politics by Bruce Bueno de Mesquita and Alastair Smith. The 18 minute video The Rules for Rulers[1] has a great summary of the principles from this book.
Dictators and elected representatives have the same problem; they must keep control of key supporters and reward them in order to remain in power.
Dictatorships have only a few key supporters - heads of the army, secret police, treasury, etc. Popular support isn't required; if these people are content with your rule, you will remain in power. If they aren't, you will be replaced.
Democracies have many more key supporters; we normally call them voting blocs - suburban voters, Hispanic voters, non-college voters, evangelic Protestants, etc. Popular support from these groups is required and this difference is why democratic governments change between parties so often.