There's nothing new here, but I think I can put it more simply and clearly than I've managed to do before.
Obviously many "democratic" governments exist, and when we normally talk about democracies, these are what we mean. What I'm talking about here is the theoretical idea of democracy, where policy is controlled by the voters. This is the distinction I made previously in Two kinds of democracy.
Political systems can be changed, either by invasion, overthrow from within the territory but outside the government, or subversion from within the structure of the government itself.
All governments devote a large part of their effort and resources to protecting themselves against being changed. It can be assumed that any governments which do not do so, get changed.
To protect the political system, the government needs to correctly identify the threats that exist to it, and devote sufficient resources and attention to resisting them. The chief premiss on which I base my argument here is that this is hard.
If those inside the government structures do not have the freedom of policy to protect the system, they will be unable to do so and the system will be changed. Most commonly, it is subverted from within, until those within the system do have the ability to hold onto power.
If the system is truly democratic, office-holders within the system do not have freedom of policy. Policy is dictated by voters. This is the line I am drawing: I am not attacking some straw-man "perfect" democracy, but any in which the voters can overrule the elite on matters of policy. If they cannot, then it is an "old democracy" and potentially stable.
Voters do not have sufficient inside knowledge of the political situation to choose the policies that will preserve their democratic power. Further, they do not have sufficient interest in doing so - the value of having a vote is in being able to influence policy according to one's preferences, and that is always likely to take priority over preserving the present system.
There are many examples of democracies voting to get rid of democracy - 1930s Germany and Italy being the best known. What I say is that democracies always vote to get rid of democracy, if not directly, then by not voting to prevent the system being subverted from within. That produces the "old democracy" I wrote about previously, in which the influence of voters is minor, and real power lies in institutions which are capable of perpetuating themselves
There could be an important exception to all this. If the franchise is limited in some way to a distinct minority of the population, then the chief threat to the system is from the disenfranchised. The voters will be well aware of this, and will have a clear and obvious interest in preserving the system which keeps power for their class. Such a system will be more stable than a true democracy with a universal or near-universal franchise.
This breaks down if there is no clear distinction between the ruling class and the disenfranchised. In that case, one faction or other within the ruling class can always benefit by a small extension of the franchise. The result is a ratchet causing the restricted franchise to eventually become universal.
Thus classical and 19th-century democracies were somewhat more stable than new democracies created today. The voters were aware that the current system was what kept them in a privileged position, and were very aware of threats to the system. From the point of view of a voter in a universal-suffrage "young" democracy, democracy just isn't worth voting to defend.
This doesn't mean that the fact of there being elections doesn't have an effect - just that the actual opinions of the voters don't.