I had this problem when I started re-riding again. it is one of those habits you can develop if you ride one horse that is well-atuned to you, maybe on light contact, maybe western, when the rein can just lie across your hand. Obviously a big problem if you want to ride on contact, or jump.
It’s possible that letting the rein fall is what the rider is doing rather than following with her hand. Maybe she needs to work on following with the hand in the two point over the jump?
It’s also possible her hands are a bit weak or arthritic. I definitely have less of a grip now on things than I used to, though I can certainly close my hands on a rein when I need to! But a friend who broke her hand a few years ago can’t actually make a first with one of her hands at all.
A big question to ask a rider with a persistent flaw is: what do you feel you are achieving with that flaw? For instance, I was having problems falling into a chair seat. When I told my coach that actually I was trying to drop my heel to feel more secure especially when maresy was threatening to buck (a bit like a western saddle bronc rider), coach showed me how to drop my thigh into the saddle instead which worked to secure my seat a lot more, and helped me stop resorting to chair seat at every emergency.
Ask your student what feels “right” about riding with open hands. She may find that riding with open hands feels like she is being “light” or “soft” or “kind,” and making a strong fist feels like she is being “heavy” or “hard” or “cruel.” In that case, she needs to learn how you take kind but clear contact and follow the mouth of the horse without balancing on the reins.
Finding out why it feels “right” to her might help her get over it.
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