But something isn't working. How do you figure out what it is?
The single biggest reason that skaters don't improve is that they don't do what the coach is telling them to do. With kids this will be about skating more, and using practice time effectively. With adults and older teens who are "stuck" it's even more basic; these skaters are often afraid to do motions that the coach is asking for-- it feels wrong (you want me to turn my shoulders how?) and they always have excuses (here are some of the ones I myself used yesterday-- "I was injured, I used to be able to do that, I haven't skated in a class in years, I've never been able to do that, I'm afraid").
While there are many good reasons to switch coaches, your own lack of progress is seldom one of them (although not never, read on!). Here are some things to do when faced with this situation:
Listen to the coach
If the coach is telling you that you need to do A to get to B, then you Have To Do A. This means if she says "more speed or you won't be able to do this skill" believe it. If she says your hip isn't open enough, then your hip isn't open enough. You cannot blame the coach for your lack of progress if you're refusing to do the basics that lead to that skill.
Listening to the coach will also help you understand if the problem is that the coach is not listening to you. If you are having trouble with a specific skill, and all the coach keeps saying is "lift your free hip" over and over, then there are two things going on: first, you're not lifting your free hip, but second, the coach is not giving you the information you need to understand what that means. A coach who's trying to help you get the skill will find multiple ways to say the same thing. A coach who has written you off, or checked out, will just say the same thing over and over.
Do what the coach is asking, even when the coach isn't there
This might mean writing down the coach's criticism, word for word.
Practice with a friend
You'll tend to skate better if you feel like you're a little on the spot.
Ask the coach why you aren't progressing
My guess is the coach will look at you like you're crazy, because you probably are progressing more than you think you are. But if you feel this way, the coach deserves to know. Maybe because you've been holding back, he's been holding back. Maybe he's been focusing too much on a skill that's difficult for you, out of both his own and your frustration with the skill. Talking to him about it may help him find a new way to teach it, or may help him think of something to teach you that you'll pick up quickly and build your confidence.
Take video of your lessons and practices
You'll notice two things-- you look terrible, and you look great. First, video always demonstrates that you don't look the way you think you look. You aren't 19 anymore. But you'll also see that in fact you're doing the skills that you think you can't do. It will also help you see what the coach sees. In three months, tape the same moves again. Compare them; have you actually progressed after all?
Parents--ask for progress reports
Ask the coach for a regular time to talk about your skater when there's no time pressure, and the skater can't hear you. Use your judgment as to whether to share the content or even the existence of these conversations with your skater.
For girls who stop progressing
Do some unannounced drop ins on the coaching sessions. I hate to say it, but girls will respond to inappropriate touching, suggestive language, bullying, or emotional abuse by withdrawing emotionally. I would like to emphasize that it might not be the coach, even if the coach is the one getting the brunt of the reaction. It might be others in the skating "family"-- monitors, other skaters, even other coaches, the management. Bullying was an enormous problem at the Ice Rink of the Damned while my daughter was growing up there. I also feel very strongly that if a child says that they don't want to skate with Coach A anymore, you should listen. No point in paying a coach that your child dislikes.
So now you've concluded that it isn't, or isn't entirely the coach's fault. I'd give it another 4 months before making a change. Let the coach know that you're frustrated (or your skater is frustrated), but you want to make it work. Get "specialty" lessons in the problem skill from a second coach which the primary coach recommends. If after four months of honest effort on both parts, then maybe make a change, with the original coach's help. I cannot be the only coach who places her students when they want to change.
Here's "St. Lidwina" on reasons not to leave a coach.
Have you ever "saved" a coaching relationship?