Maybe we should start with defining democracy. Even within political science, there is real disagreement as to how it should be defined. Once we know what we're looking for, we can better ascertain if we have it or what we have is an illusion of it.
Some clarification on other terms used here. A republic is simply a state that does not have a monarch at its head.
Democracy, as I think you are defining it, LJ, is a liberal democracy, the democracy of all democracies, an ideal type. None exists and none will ever exist in that form because ideal types do not exist in the real world. We can only aspire to them This, of course, should not be an excuse to justify the failure of a state to examine how far it has reached along this path to getting close to this ideal type.
A democracy, in its most basic form is a country that has competitive elections to important executive positions. More countries than we would like to think meet this condition. More do now than ever before, that itself is heartening.
A liberal democracy can be defined as a country that possesses:
1. Competitive Elections
2. Rule of Law
3. Separation of powers
4. Respect for civil liberties
Most countries fall short of this second definition. Even the Western democracies in which most of us reside fall short of meeting this ideal type much of the time. A case in point, the most recent Economist has an article on Amnesty that addresses human rights abuses particularly in these Western democracies and by these Western democracies in other parts of the world.
There are two ways in which people can have a say in democracies -- only through elections and some form of referenda for direct votes on policy issues. The first exists and we do have a say in electing our representatives. That is how most democratic institutions are set up.Everyone knows that the people never have a say in anything important. Not even during revolutions. It is only the leaders - corporate, religious, political etc - that rules.
Take the case of California, on the other hand, where people do have more of a say, more regularly, on actual policy issues. I'm not convinced their system of direct democracy works better. Proposition 8 and the problems the government is having in even correcting budget issues is pretty crazy.
The ideal type you speak of not only has perfectly responsive institutions but it also has perfectly responsible citizens. Perfectly responsible implies perfectly informed. We don't meet the ideal type necessary for this perfect democracy, how can we expect our institutions to meet this impossible ideal type?
Finally, it may interest you to know that the Athenian democracy did not only NOT allow women and slaves and people who did not own land to not run for elections but also not all senators were elected. Many of them were pulled through a form of lottery. Yes, names out of a hat, ladies and gentlemen.