First of, I have to correct you about the Greeks. Only pure greek citizens were allowed to vote. If you lived in ancient greece and weren't greek, you didn't get to vote. You also have to understand that there was a lot less people in that time so much less votes to count and it was basically easier.
Democracy isn't dying. Democracy is...evolving. For the better or for the worse, that we'll see. Pure democracy is impossible to achieve.
Here in Canada, we have the same type of representative government as in the UK.
I kinda know what you mean when you're talking about our representatives not doing exactly what we would want them to do but when you voted for him and got him elected, you've given him/her your voice among your peers. He is supposed to represent you.
Of course, unless you're strangely lucky, your views on every subject won't be the same as him/her's.
The government disagreeing with the people is common in every democracy.
This bring us on the people voting for the laws themselves. How is this supposed to be done? It's totally impossible. People don't have the time to go vote for laws all the time. People will simply not care about it and let the crazy extremists vote for their laws.
Now saying that because the US went to war for "freedom" and "democracy" kills democracy is false. It destroys diplomacy but not democracy.
Believe me you don't want to live in a totalitarian country. Democracy is way better. Unless you're asian...(bad sarcasm, I'm asian myself don,t call me a racist).