I just loved Scoutrider's explanation of the slightly counterintuitive way that you must have your body; NOT leaning back but rather having the hips ever so slightly angled forward. WhY? To make an openning under your seat so that the horse can come up under you with their back, which will naturally occur if the step back under by lifting their feet, rather than draggin them from a stiff and inverted back.
IN any case, back to you and YOUR situation; one thing that you can do to break up a horse that is resistant to backing it to use one rein much more than the other. Start asking to the backup with two reins, your body and light, alternaiting legs (alternating IF she is actually moving backward, so they follow her barrel), . Have one rein be slightly more active than the other and look for your horse to have a little flex in the jaw toward that side. If she only braces or throws her head up, then take in THAT rein and create a bigger bend , so that she is effectively backing in a circle. This will disengage her hind quarters. WHY? To break her out. She gets stuck and if you fight her with more even pressure, she will just brace evenly. But pulling her on one rein only will break her out. Once she has disengaged, you probably will feel her head come down momentarily. Ease off everything, then reposition for another try. Don't worry if she is no longer backing in the direction you want to go. ALL that mattters is that she back up when asked. So, ask again, lightly with one rein a bit more active than the other, and if she reisists, take her into a backup circle. If she thinks about backing up and you feel it, give a tiny release, a praise and then reask.
Also, try more work backing her on the ground , while facing her and while standing by her side. If she has trouble on the ground, be sure that there is now comfort issue involved. Being unable to back up is a sign of chiropractic problems, though I am by no means saying this is your case.