What you can do is set a variable to the map so every encounter increases it by 1 and then have an event that is a parallel process that checks for when the variable equals 15 and then it changes encounters (3rd tab > system settings) to false. This would work well with some tall grass type event so that each battle will raise the counter. You just have to make sure that once the player moves to the next map encounters is returned to true.
Also, if you have the event turn on a self switch once 15 is reached, then you only need one variable. The only downside to this method is that the counter will be returned to 15 unless that number is reached, but it's worth not wasting so many variables for each map.
If you want the battles to occur on the map and not through events, then you'll something much more advanced like a script just like bgillisp said.
Sorry if most of that doesn't make sense. I can't explain things very well. Anyways, good luck!