Once I got over the vertigo from watching that video, I could see that the way
stayed on is that she stayed vertical (which means she leaned back), and she allowed her arms to go forward, and the reins to slide through her fingers; jsut as
One thing will make that difficult and this is if you already are holding the reins with your elbow straightened out and your arms stiff and extended to the max already. There should be some bend in your elbow, and your upper arm closer to vertical, tucked against your ribcage more than sticking out like you are holding a wheelbarrow.
When you get better, you will be able to set your horse up so that when she transitions down from a canter to a walk, you will prepare her, and she will do so in a more balanced manner, so it won't be so abrupt. This takes having the ability to put her onto the bit some, and to drive her forward with MORE impulsion. In fact, if your horse is canter faster, she may actually trip LESS.
I had a fall off a hrose, when it did just what waresbear's horse did, but I was chucked into the ground ( I do not have as good a seat). It was a rough fall, and I was scared to canter for a long time. When I did canter, I allowed the horse to just sort of lollygag along at a sloppy and lazy pace, and so he would still trip. When I picked up the energy level and asked more of him, he tripped less.