Representative democracy is still usually referred to as a Democracy. This is just semantics.
Not entirely, it is a democracy, but not a direct democracy. It's built off the assumption that not all voters have time to vote on everything, and as such select someone who's supposed to represent their interests.
That said, the american implementation of a democratic republic relies heavily on area based majorities and may very well not represent as much as 49% of those who voted in their election. Possibly more if there's a strong 3rd party in the area.
In theory that one person is supposed to be accountable to the voters. But almost no one has trouble with their guy, it's all those other people's guys who are the trouble.
Edit:
Audit Rand Paul!
