Your thread title asks "What would it take for you to stop supporting representative government?"
My counter-question is: As opposed to what?
The situation in Brazil brings this question to mind. The President's approval rating is 10%, the population has a "free stuff" mentality, corruption is rampant, the economy is about to slip into a 1930's-style depression. Many miss being ruled by the military junta.
Your OP offer is a military junta? The many who miss it are those who profited most from it. The rich who were immune to abuse, the soldier families who could lord it over the rest of the population, and of course the members of the junta itself who had absolute power.
I've also seen some members argue for other forms of authoritarian government. Monarchy, Dictatorship, etc.
The argument (which has some minor merit) is that most people are too self-centered to think in terms of the good of the many. They are so focused on trying to make their own way that they have little or no time to think about anything else. As such they can be easily led like sheep; so why not let the best people lead them? The cream at the top.
The problem with this is that the cream at the top are often the most successful at being selfish and self-centered. Sometimes by hard work, but just as often by just plain luck they have the kind of wealth and security that gives them the leisure time to think outside the box. This does not necessarily make them good leaders, as we've seen time and again demonstrated throughout history.
Representative government is the best option out of a lot of bad options. It gives anyone the opportunity to rise to leadership from among the masses. IMO people who seek more authoritarian forms typically believe they know what's best for everyone else, and they would be among those best suited to lead the herd themselves. Why get elected? Just be born to it, or maintain power by using mercenaries and brute force.
I don't think we need more centralized power. IMO an educated, informed population with an opportunity to participate in representative government beats any government that "makes the trains run on time"
at the point of a gun any day.