Technically speaking, the government of the United States is a republic. It is, however, a democratic republic, a fusion of two different types of government in the attempt to create a sort of balance between the goods and bads of both types of government. In this system, how well the government works depends largely on who's in charge, the feelings of the community, and several other factors, some more influencial than others.
The people who wrote the Constitution way back over 200 years ago knew that things change all the time. Heck, they were even loyal British colonists at one point, and now they had a new, chaotic nation that needed a strong foundation. They knew that if this could change, so could other things. They included an ammendment process to make sure that people could not simply say, "It's not in there, so it's not legal" and not get a bill supported by the majority passed by this reason. This way, it would still be viable even 200 years from now, as future generations could add things that would apply to them that the framers could not possibly even think of.
While it may not be the brightest time in American history right now, great good came from this process. Slavery was outlawed and women got the right to vote, for two. Just keep in mind that the U.S. is still a young nation when compared to the rest of the world. It still has a long way to go until Americans find out the way that works best for them, but as long as they can learn from the successes and mistakes of other nations, along with their own, it will become closer and closer to political equilibrium.
...that's what I think, anyway.
By the way, I'm no good at history, so correct me if I'm wrong about some historical facts.