I'm not myself at an axel level, so I can't comment on such things. But, as a person who has taught figure skating group lessons - though only on a voluntary basis - I would say that in the first few sets of classes, several major factors apply to figure skating group lessons, in descending order of problem frequency.
1. Some parents don't get their kids to lessons in time, or they miss a lot of lessons. They miss too much of the teaching and in-class practice. This is probably the biggest factor.
2. Some parents don't bring the kids to the ice in between lessons. You can only go so far without practice.
3. Some kids just don't care. E.g., the typical hockey boy whose parents think he will skate better if he takes figure skating lessons. They usually spend all their time picking on the girls, instead of paying attention or practicing. It doesn't help that most of them are already better skaters than most of the class, at least in those skills they care about. In addition, at a late pre-teen or early teen level, some girls who have been interested in skating up to that time, start spending all their time on the ice standing by the boards, gossiping and giggling with each other. That applies even to moderately high freestyle level skaters.
4. Most kids or parents don't tie the skaters' boots tight enough. This is a lot more common than people realize.
5. Some kids have skates that don't fit, or are not mounted to be properly balanced to their feet.
6. Some kids don't have properly sharpened skates. There is a lot of overlap with #5, especially if they are using rental skats, which are often pretty useless beyond basic forward and backwards strokes. I recently tried using the rentals - it was AWFUL. Nothing worked.
7. Some coaches are not very good at teaching, or are only good at teaching to students with specific learning styles. At the most basic levels, there is only a little correlation between skating skill and teaching skill. It is amazing how many very good athletes have trouble teaching people who don't understand what to do just by watching. And a few coaches teach some things wrong.
8. In the same vein, some kids have the wrong learning style for their coach's teaching style.
9. Some coaches only pay much attention to the best students, or to the students who ask questions.
10. Some kids have trouble paying attention to directions, or are easily distracted. There is a lot of overlap with #3, 7, 8 and 9 here.
11. Some kids aren't strong enough or coordinated enough to do basic skating. This is sometimes true at about age 4, and is quite frequent at age 3 and below.
12. Some kids have more "natural talent". Some of this comes from prior athletic activities, like dance and gymnastics. I believe some of it is genetic. You don't need a lot of natural talent to get through BS2. But people start dropping out in large numbers around BS3 (especially if they have trouble mastering outside edges), or can't pass it by reasonable standards. (This differs by rink and instructor, because some instructors have a lot tougher standards than others.) And by the time you get beyond the most basic jumps, some kids can't do it no matter how hard they try. (Neither can I...)
13. Some parents distract their kids while they are in lesson. It's not all that common - but it is an extremely hard to overcome problem. I know this is mean, but: parents - stay out of the way during lessons.
14. Money. At the early levels this isn't that big a deal - especially since the program I was in offered free lessons if the parents demonstrated need, and they got their skates sharpened free too, but by the time they need private lessons, it becomes important.
15. Some kids are afriad of falling, and are constantly scared and stiff on the ice. Not nearly as frequent with kids as adults, but it happens once in a while.
Anyway, that is my take. I don't think it is much different from why students have trouble learning other skills and subjects.
I'm not even counting the unavailability of ice time or coaches to people in some communities. That's a given.
I'm not sure how important school studies are in this vein. I've been shocked by how many hours high school students spend on homework now - often 6 - 10 hours per night for the college bound crowd, plus other after school activities, and required community service. I suspect a student cannot hope to spend enough time on the ice to be really good if they do that. Trade-offs exist.