Remember that if your mechanics are good, your arm just comes along for the ride when you throw.  This means that increasing stamina has to start with your leg strength for torque and stability, and core body strength for rotational force.  A weight training program for legs and core body will increase stamina.  This along with improving your mechanics will give the added bonus of increasing velocity.  Lighter weight training for the arm (especially the shoulder) will help prevent injury.  And don't forget to stretch stretch stretch!

I should have clarified that I was referring more to the legs and torso for stretching, however I've always had success with very basic stretches for the arm and shoulder that are recommended by trainers and orthopedics (pulling the thorwing arm across the chest and behind the head).  But I've always believed the best way to loosen your arm is to throw.  Every winter, before I'm back in shape from the 5 month lay off, I throw hundreds of BP pitches (many from 60 feet and in excess of 70 mph) at least 2 times a week.  I rarely experience much arm soreness but until I build up my stamina and strength and regain my flexibility, it's common for me to have very sore leg and torso muscles the next day.