Can you run away without losing against a monster?
No, you cannot run away if you are winning with just your equipment. From the Munchkin FAQ:


  Q. Do I have to kill a monster? Even if I'm winning, can I just choose to Run Away?
  A. You can't Run Away if you are winning with what you have in play. However, you are not required to play one-shot cards, negative Monster Enhancers, etc., to beat it, even if you could win handily. So, in that sense, you would be able to choose to Run Away.