I liked what Kevin had to say. I grew up in a very active family. My dad was always the kinda guy to throw a kid in the water and say "learn how to swim". I was swimming at 3 months, my brother at 5 months. I was dirtbiking by age 5, slalom skiing (water) by age 7. If we ever showed fear, we had to hit it head on and get through it, with his help of course. Shoot, I can remember skidding across the water on my face thinking "dad said not to let go of the rope!". Is it the most common form of parenting, no, and many experts would probably disagree, but my brother and I both learned that the only way to make fear go away is to do whatever it is that you are afraid of.
Riding was my passion (and still is), but not my families. But of course they were supportive. My dad and I worked at my trainers house every weekend in exchange for me leasing a horse. I was 13 when I rode a qh mare named Mom. Mom had chucked me into jumps multiple times, and fear was starting to take over. The jumps started getting lower, I became more tense and more fearful. One day, dad came out to watch me ride. By the time that ride was over, my face was soaked in tears and that mare was going over every jump in the arena without a glitch. Fear wasn't an excuse. He wasn't a horseman, but he also wasn't going to let his daughter back out of something that he knew she was capable of. It wasn't long after that that I started working with problem horses.
Was it a risk, yes, but if the passion that I had wasn't strong enough, I wouldn't have stayed in horses anyway. His confidence and faith in me is what made me know that I could ride that horse through anything, if he had backed off, then I would have known that there was reason to be afraid.
I'm not saying to scare the stuff out of your daughter to eliminate her fear, but I am saying that you have to challenge her, like Kevin said. For me, I could walk, trot, and canter all day long, but those jumps terrified me, so that was the line he pushed. Find her line and push it just a little bit each time. Make her believe in herself and that horse. If her line is getting on the horse, that is what you work on. It just has enough to keep challenging and keep building confidence. It has to be something to keep her wanting more. If she has lost interest after one fall, then the true interest was never there to begin with, and I would encourage her to pursue her dreams instead of yours. Lack of interest is a reason to quit. Fear is a reason to learn and try.