1. Arthritis has already been mentioned - it is a primary reason why a horse is not willing to pick up its hooves.
2. Laminitis or founder.
3. Any sort of skeletal injury/discomfort that makes it uncomfortable to stand on three hooves.
3. Allowed to get away with it.
Lots of good advice on HOW to get the hooves up so you can clean them but first you need to figure WHY she doesn't want to pick them up.
I have one horse, for example, that sometimes has to be leaned against the stall wall to pick up his left hind hoof for trimming. When that happens, I know I need to call the chiropractor to re-adjust old back injuries.
That is something an experienced horseman, standing right there with you, needs to help you figure out