Multi-player-games are not always shown in the normal (all / user / my) (finished / running / observed / observing) game lists. They only show up if you are at a specific moment visible as black or white player. For multi-player-games, the black and white players rotate through all participating players. So when you are rotated out, the game will vanish from your normal game-lists.
 
This design was chosen (even though it is less intuitive for the users), because integrating MP-games into the normal game-lists would basically require re-inventing major parts of the server and game-handling.
 
To compensate there are special searches to find and list multi-player-games:

• How can I find my multi-player-games in setup-mode?
  
• How can I find multi-player-games?