There are many reasons to avoid levels; one simple one is you like the level you're at1).
The first way to avoid gaining levels is to not go to the dojo2).
The second way is to go to the dojo when you have almost no hit points3).
The third way is to sell your weapon (or armor) before the "New Day4)."
The fourth way is to hire Bruno the Bouncer from the Mercenary Camp in IC. He will happily keep your master away for as long as you retain his services. 5) It costs 30k req to rent Bruno.
The fifth way is to bribe Dan with a number of cigs equal to four times the level you currently are. In return, he will serve you an "American Beer" which will leave you feeling weakened (and knock your exp down to the minimum amount needed for your current level.)