Exactly how old is the mare? Is she on any kind of joint supplement or does she have a documented history of issues that could hinder her in more strenuous work? First and foremost, eliminate pain. Can she canter at liberty, in the pasture, on the lunge?
If all pain is eliminated, your problem sounds like a lack of balance or strength to maintain the canter with the rider in the equation. Trot work is great for building balance and preparing for canter work - practice really riding the trot, doing lots of figures like serpentines, figure 8's, deep corners, spirals, eventually more challenging things like half and full voltes. The better and more balanced the trot, the better prepared for the canter she'll be.
Next, don't push her to canter laps around the ring. Work on the transition, getting that nice, and take her back down to the trot before she falls back. Let her build strength a bit at a time, and strive for quality, not quantity.
I also recommend enlisting the help of an instructor, if you haven't already, to work with you in person. This can be a frustrating issue, and having someone who has dealt with this type of thing before to help you tweak your riding to help your mare can be invaluable.