Pandemic Legacy: lost characters
From the rules (page 4, emphasis added):


  Each player has a specific character with special abilities to improve the
  team’s chances. Each player begins game 1 by creating a character.
  
  To create a character: Select a Character card (each one has different
  special abilities) and give your character a name.
  
  These characters will carry through from game to game and they may
  become lost (see below). You do not have to play the same character in
  every game.


And, from the Compiled FAQ on BoardGameGeek:


  If your character becomes lost, destroy that character. Discard your player cards and become a Civilian, and place your pawn in any city with a Research Station; if you had actions left, you may take those actions. At the start of the next game, you can choose a character (from those left) as normal, if there are not enough Characters left, some players may need to start as Civilians.


So, once a character is lost it can never be played again, and if there are not enough characters available for the number of players then you will have to have some players use civilians instead. However, there is no general requirement that you have to keep using the same characters over and over even if they don't get lost, so you can always change characters each game.