Which principle of the US Constitution is most important to preserving democracy?

It depends on how you define democracy.

If you are worried about the presence of voting, then the principle of having regular elections and a peaceful change of power between political parties is the most important principle.

If you are worried about people being able to use politics to improve their circumstances by using their vote to pick a person who coul represent them, then the First Amendment's free expression principle and freedom of religion, freedom of assembly, and freedom of petition are the most important principles.