She probably just needs the proper muscles to actually pull off a canter. This way, she can get into it...get the muscles and the praise.
I totally agree with this!!! My mare wouldn't canter willingly on the lungeline OR during round pen work. However, up till I got her last year she hadn't been worked, as she had developed some behavioral issues that were way beyond the owners she had at that time. She wasn't sore, so I figured I would just work on solidifying walk, trot, stop, etc on the lunge and round pen. She then had nearly 5 months off (due to my own health problems), so has "just" gotten back into work about 7 weeks ago. Well guess what? She canters on lunge, in round pen, and under saddle quite willingly now-she did before, but not 'comfortably'. She is also in superb condition, compared to what she was when we started out, hahahaha! I can also do smaller circles in trot and canter, than before, as well, and I really believe that's due to me taking the time to build her body condition back up again, and giving her muscles a chance to get strong, helping her balance better.
NOW, that said...I'm not sure how you are cueing for your canter, but be consistent, and always start out 'soft'...ie, something like a "kiss" or smoochy noise, if there is no response, use your legs, and if that don't work, use a crop. Don't immediately start kicking and cropping, because that's why horses become "dull" to our aids...when we do it, but have no 'meaning behind it'... I would also start getting her more responsive on the ground in the canter before you attempt undersaddle; if you keep getting on, and consistantly NOT getting the response you are wanting, that is only going to keep the behavior going. Teach her to respond to a 'vocal cue' from the ground, and then use it from the saddle as well. It's easier 'shown than explained'...hahahaha.