Sonnys right. You might be telling her to stop without even knowing it. My warmblood was in dressage training at a young age and was taught to stop when the rider put weight in their heels. Well, I don't do that, personally I don't want weight in my heels (just in my seat) so I had to teach him my way of stopping.
I would triple check saddle fit, even get someone who is very accurate at saddle fit come and take a look. She might be in pain, the saddle might be pinching her, or she could be out of alignment, etc.
Check your fluidity while riding. Do you bounce, brace, or are you soft, fluid and do you have an independent seat? Sensitive horses will sometimes stop in the rider is not in harmony with them, it's their way of saying, "Hey! Get your act together will ya?!"
You can't blame them.
If you can rule out all these things, physical issues as well as rider issues, then you can work on the behavior shaping exercises. When you ask her to go gently squeeze her, don't kick. Allow the squeeze to slowly work down from your theigh down to your heel, then turn your heel out and down, then start creating commotion above her, like swinging a piece of rope. "Slap" yourself first across the shoulders and then irritate her with the rope. When she goes release all pressure. Say you are trotting and she stops. Go through these "phases" of pressure. Each time she stops make the interval in between each "phase" a little shorter, but only AFTER she knows the pattern. Remember you are teaching her, so you have to be patient. You need to be effective to be understood, but you need to be understood to be effective. This will teach her that it is HER responsibility to keep going until told otherwise. It's actually a pretty easy issue to fix.