Why do the skill tests disappear when you can't pass it several times?
If you're referring to the "test out" buttons within the skills, those are not intended to test you on the material you're learning. They're there to find out if you don't need to learn it. If, as you say, you weren't passing them, you probably shouldn't be trying to skip that section, anyway.
I think the only real test of your skill is the quiz you can buy in the lingot store, but that tests you on the whole tree, not just the parts you have already done, which throws some people.