Quite often, horses in some degree of pain will have a hard time backing up - it just hurts to shift the weight and move that way. First thing to check out is a chiropractic, muscle soreness, or saddle fit issue. Even on the ground, a poorly fitting saddle can cause lingering discomfort that make backing up hard. The mouth is a potential spot to check as well - sore teeth can also cause horses to be "disobedient."
From there, I second Saddlebag's method on the ground.
In the saddle, I've found that the way that the rider is sitting makes a huge difference in how the horse responds. Never pull back on the reins to back up - you're only closing the front door, disallowing the horse to come forward. Apply a little leg, and make sure that you are sitting tall. Tip you pelvis forward a bit, putting more of an S-curve in your back than your normal neutral riding position. Ask for a step at a time, rewarding the smallest change and the slightest try, just as on the ground. Doing this, rather than just pulling on the mouth, will help her to come back smoothly, with correct weight distribution, roundness through her topline, and cadence, rather than just inverting and evading backwards.