When I was shooting in college, improving archery stamina involved a lot of shooting and something we called SPT or Specific Physical training.
There's not much to increasing shooting capacity. You need to shoot a lot. A standard FITA is 144 arrows + warm up + maybe sighting rounds. So practice for competition should included at least 200 arrows as often as you can manage. I could only ever manage 1200 - 1600 arrows a month and that is fairly low. Your aim here is to be comfortable shooting significantly more arrows than a tournament in a single session.
In between shooting you can do SPT. This involves drawing your bow with no arrow and holding your form correctly for 30 - 60 sec (or as long as you can). Then rest for double the hold time. Go again. Try and do this for 30 mins. This is pretty hard so slowly build up to it. Don't expect to complete the exercise as prescribed initially. You may want to do the other arm just to keep things even.
Ki Sik Lee's website and book Total Archery are also worth reading.
You'll also want to do some general physical fitness to even out all that pulling and also cardio.