I was doing this the other day and on about the 10th jump the kite drifted upwind over my head at 12 oclock as i landed, stalled and just floated to the ground. landed right downwind tho in the powerzone which made me wonder what would happen if it suddenly powered up again? (probably something bad right?.... haha).
I just hope you are in the water when you find out what happens. I'll give you a hint though...from my experience with two kites, I have found that when a kite Hindenburgs, by a lull in the wind, and then falls down (stalled, as you said), and gets hit with a gust, when it is about 15 feet off the water, the kite will take on so much power in a split second, that the kite will be ripped completely in two. And that is the good part of what happens. The bad part is what happens, just before the kite rips, to the rider...swan-diving into the air and then the bottom, head first.
This is situation where the kiter gets only a split second to decide whether or not to throw the kite to its safety. After you have had a couple of kites get ripped in two...and come close to breaking your neck, you will always err on the side of throwing the kite to its safety, rather than betting against a gust hitting the kite. I hope you are on the water, where there is some cushioning for your body, when you learn this. On land, you are garrenteed of an injury, or worse.
Best of luck to you, in surviving your initial learning and experimental period.