The patch for the second living story season gets released next week (2nd June 2014). As part of the changes, ALL living story “episodes” will have some permanent content that essentially extends the personal story of all characters on your account.
You’ll need to log in once each cycle (so once every 2 weeks) to unlock the new story missions on your account. Then the unlocked episode will be permanently available to any character you ever create.
ArenaNet: Introducing the Story Journal.