Can a new player join a group only when a new campaign starts?

I moved into a house share with my friends (ages 24-29), and they play role-playing games on weekends at the house, but they won’t let me join in because they say it’s not fair to the players that have been in the group for a while. Specifically, it seems that it’s not fair on the DM to have to write in a new character. I can understand this, but one of the members dies nearly every month and has to write a new character.

As a newcomer to role-playing games, I’m not sure how this all works. Is it usually necessary to join a group when the group is just starting a new story? Or is it possible to join an existing game?