Some horses are not strong enough in the back to pick up canter with a rider on their back. I would be lunging her doing extensive trot-canter-trot transitions, working her on hills and REALLY focussing on getting her hind legs stepping under her centre of gravity, and her back swinging through. If you can build up some muscle, this will help her take your weight in the transition.
I would also question how you are sitting. It is possible that you are weighted slightly crookedly, or maybe you are being to 'loud' with you seat and aids. I am riding a mare at the moment that will NOT canter, will NOT half pass, will NOT stop, unless you ask with exactly the right aid at exactly the right time. If you are crooked in the saddle, she will run straight through you and drag you around the arena. The second you fix your position, she is soft, uphill and through.
Some horses are just very sensitive to the aids you give, and you may need to really think about what your seat is doing. Like how we say men think with their 'little men', you need to think with your seat!