The letter box is the anchor of the story's foreshadowing of "something" that will be filtered through the everyday life of Nora and will change her forever. The moment we find out that she has been blackmailed, the letterbox becomes the center of attention: It is the potential agent of chance that Nora is dreading so much, and which will change the course of the story, and of her life. Considering that letterboxes are the main key of communication among upperclassmen and women, we can almost see how throughout the play, this very important communication device (where people leave infromation, introduce themselves, and place their "calling cards) had not become so available, just like Nora had not openly communicated her situation, or her real self, to her husband.
When reality finally hit and Nora's life as she knew it depended on whether the letter would be read or not, and whether the letterbox would be opened or not, we see how the fact that the letter box was both open and closed and then opened again is similar to Nora's own secret ordeal.
I believe that Ibsen uses the Letterbox to show the childishness of Nora. Little children try to hide their little mistakes. However, children are never able to keep them hidden for long. Just like a child, Nora tries to distract Torvald from her glaring mistake. Nora dances and begs Torvald to not look in the letterbox. Despite her efforts, the letter does not simply vanish or dissappear. Nora thinks that by ignoring her problem, it will cease to exist.
let it be for free you faggets