Betrayal at House on the Hill - Mystic Elevator
There are errata pertaining to the mystic elevator, but I don't believe that they would fix your situation:


  Mystic Elevator -- Can a group of heroes or monsters use the elevator in a group to
  attack their enemies, then retreat to safety?
  
  
    No. Add the following rules:
    
    
      
      Monsters and traitors can both use the Elevator to go wherever they wish without
      rolling. However, the elevator may only be moved once during each entire
      traitor/monster set of turns, the first time a traitor or monster enters it. In other
      words, if the traitor uses it during his turn, then it will not work later on if a
      monster enters it.
      Heroes must roll for their destination floor each time they enter the elevator, or at
      the end of each entire movement phase that they spend in the elevator without
      moving.
      
    
  


If I understand your question correctly, you are talking about a monster using the Mystic Elevator just once each turn; and because of this, you couldn't ever catch the monster. The thing is, this isn't a situation unique to the Mystic Elevator. Depending on the layout of the house, if you only have 1 movement, and the monster has more than 1, then it would be easy for the monster to always avoid you, even without the Mystic Elevator. 

If the win condition for the traitor is simply to have the monster survive long enough, then it sounds like a clean with for the traitor. If the win condition requires the monster to kill the heroes, then the traitor shouldn't be just running away the whole time.

To advise how to handle your specific situation, we would need to know the actual win conditions for both teams. But if the game cannot end without the monster and hero fighting each other, then it sounds like a clean stalemate to me, and a legitimate move for the traitor to make if he is sure he can't win in combat.