By this mare's reactions, it sounds like she has either learned how to evade backing cues, or just was never really taught how to back under saddle. Retraining, or training her to back is the same, really...I prefer to do in a snaffle bit, but that is your choice.
When I teach a horse to back I don't use 'tug and release' methods on the reins, I use light steady pressure, and only release when he gives me what I am asking for...a step backwards. I cue from right at the cinch, and use a deep seat, so the horse knows he is not to travel foward. Don't pull harder on his mouth if he doesn't respond immediately, just keep your pressure even and steady until he gives you what you are asking for; same with your leg pressure...don't kick and nudge harder...just keep the pressure there until he figures out what it is you are looking for. Eventually you will get a quicker response, and will be able to ask for more consecutive steps in each set, but at first, just ask for one step, and then release all pressure.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."