I would be she doesn't know what she's doing. She's asking him to go forward, and tightening her hands at the same time. She needs to give him head head, maybe bend him a little, and try and get that forward motion. We know NOTHING about the pony/rider background though, so it could be anything. He could be sick of that arena or have something pinching for all we know.
I don't see anything wrong with staying on, she has a pretty good seat! I would just change the way she is working with him IF other problems such as pain aren't at work. I don't feel "disgusted" by this video, it's not like she's abusing him.
Every great dream begins with a dreamer. Always remember, you have within you the strength, the patience, and the passion to reach for the stars to change the world. ~Harriet Tubman