I believe that representative democracy is an excellent form of government. Having been born and raised in the United States, and lived here all my life aside from a few fairly short overseas trips, that's probably no surprise. What may be surprising is that I'm less sure every year that the United States actually is a representative democracy in practice.
But are the people being chosen really representative of the people? That's the part that seems to be falling apart, for a wide variety of reasons. I don't pretend to be an expert on everything that goes into this issue, but I can list a few things that seem to be especially egregious problems, even to a layman like me.
Gerrymandering. This is the practice of drawing electoral districts such that one particular group, usually a political party, has overwhelming support in that particular district. This means that anyone who votes in that district who doesn't support that group is effectively cut out of the representative process. Even worse, it's possible to draw the boundaries such that one group gets more total districts, even if there are actually an equal number or even more voters for an opposing group. Since representatives have equal power no matter which district they come from, one group ends up controlling the government even if another group has equal or even higher support.
My home state of Michigan is heavily gerrymandered in favor of Republicans, as this article does a good job of explaining. In state-wide elections (i.e. US Senate, President), Michigan has consistently voted Democratic for years, indicating that the majority of voters lean Democratic; yet in district-driven elections (i.e. US Representative, state representatives), Michigan consistently sends largely Republican representative groups. Gerrymandering isn't the only cause, but it's a major contributing factor.
Party Control. The voting process is largely controlled by the two major political parties, Republicans and Democrats. They set up primary elections to choose their candidate, and voters overwhelmingly support one of those candidates. In many places, in large part due to gerrymandering, the primary election effectively chooses the representative. Third parties do exist, but they generally have such low visibility and lack of power that voters aren't even aware of them. There are options for mitigating this issue. For instance, holding a blanket primary, in which the primary process is not split by party. Better yet, a form of proportional representation would allow even small parties to have some level of representation, and if properly implemented would address some of the gerrymandering concerns as well.
Term Length/Election Frequency. We in the United States have elections regularly, choosing every type of representative from local school boards to the President of the country. There's elections every year in most places for local concerns and every two/four years at the national level. On the surface this seems like a good thing; the more often we vote, the more attention the elected officials spend making sure their voters are happy. Unfortunately, what that means is that the officials tend to look primarily at short-term actions which make them look good at election time, regardless of the long-term consequences. Often they spend more time raising funds for the rapidly-approaching next election cycle than actually governing, especially when terms are only a year or two in length. When you have to be voted into office every two or four years, it's very difficult to look out five, ten, or more years and do the best thing for the country in the medium-to-long term, especially if it causes some short-term pain.
Campaign Funding. Rules for election campaigns in the United States seem fairly strict on the surface. There are all kinds of rules about how much money can be accepted, how it needs to be reported, and how it can be spent. Those rules have been regularly weakened, though, most famously by the Citizens United Supreme Court decision in 2010. Organizations known as "Super PACs" allow unlimited funds to be spent to support (or oppose) particular election campaigns. In some cases, there's no requirement to disclose who gives the money. The reason all this is important is that the voices of those supported by the big money drown out all other viewpoints.
Issues like those I've mentioned here (and others, like voter registration restrictions), are limiting the actual representation of the will of the voters. I'd love to support politicians who are dedicated to making improvements in the electoral process, but it seems they're all busy benefiting from the system rather than trying to change it. I still vote, because I consider it both a right and a duty, but it sure feels like a useless gesture sometimes. I can certainly empathize with those who don't vote at all.