This is not unusual. I would just thank her for training with you for as long as she has and let her go. You can ask her if she could give you a testimonial (if she hasn’t already) and maybe she will refer others to you in the future. Everyone has their own personal reasons of why not wanting to continue.
You’ve received good commentary so far and I’ll try to go over new ground.
1) Is this the only discussion you’ve had regarding her progress and satisfaction? Wiser trainers than me taught me that feedback and renewal discussions shouldn’t wait until the end of the package. As we celebrate successes, we talk about future goals and I get a sense without being pushy whether my assistance is part of that future-casting.
2) You might send a very short thank you and in it ask, “Would you be interested in providing a short written testimonial about what you liked about my training style so future clients can learn about me?”
even though this is a strange situation, I would not ask her any questions. Just thank her for training with you.
There are so many things that we don’t know in this scenario. But as you are already at this crossroad with this client, the most that I would suggest is to email her with a thank you of your own. Express that you enjoyed training with her. Leave the door open for her to contact you whenever she might want to in the future. If you have a newsletter, you could ask if she would like to receive it in the future.
It may just be that she feels upto exercising on her own. Do you feel she still needs your assistance? If so, tell her this in the email and why. She may have had a change of finances. It can be distracting to dwell on the possibilities. The only other way to find out her reason for discontinuing is to ask her directly. Whatever you decide to do, keep it to the point and professional.