It's a continuous struggle, and one we're not yet finished with, so there are plenty of examples to choose from. Here are a few more to add to the list:
1) 1798 - Alien and Sedition Acts passed, which were clearly unconstitutional, yet the Supreme Court did nothing. Our democracy could have faltered right then and there.
2) Election of 1800 - first peaceful transfer of power between political enemies. John Adams honored the results of the election, almost unprecedented at that time.
3) Seneca Falls, New York, 1848 - The first women's rights convention, and the first public call for women's suffrage.
4) The Civil War - Abraham Lincoln arrested people without trial, instituted an illegal income tax, and ignored the Supreme Court, all in the name of saving the country.
5) 1950s Desegregation - Trying to enforce the Brown vs. Board of Educationdecision integrating public schools and facilities. It took nearly two decades to accomplish that.
I would think that one of the most obvious examples of a struggle for democracy would be the civil rights movement of the 1960s.
One book I use to teach American Government (coincidentally called The Struggle for Democracy) says that there are three aspects of democracy -- popular sovereignty (the people rule) political equality and political liberty. The civil rights movement pushed for progress in at least two of these areas.
During that movement, African Americans and their allies worked to try to make African Americans into full partners in the American democracy. For example, they worked to give African Americans a part in popular sovereignty. In other words, they worked to give them the right to vote -- to help rule by helping to choose leaders. At the same time, blacks were fighting for political equality. They were trying to get treated the same way (by the law) that whites were.
In these ways, the civil rights movement showed African Americans struggling for at least two aspects of democracy.