Well, sometimes the problem isn't that your horse is unwilling, he's just unable.
Sonny might need to put on some muscles before he is able to sustain a slow jogging frame. It takes muscle for them to move that slowly. I always use the car analogy:
Imagine that Sonny's gaits are like gears in a car. Usually, the slower the car moves, the lower the gear. But now you are asking Sonny to move more slowly in a high gear. There are cars that can pull off from a standstill in 5th gear, but they usually have around 400-500 lb.ft. of torque. Otherwise they will just stall. Sonny is in the same position -- he may not have enough power to keep up a strong frame, and so he is increasing the speed to make it more comfortable for him. In order for Sonny to jog with a nice collected frame, he will need to have the muscles to support himself.