Why do the skill tests disappear when you can't pass it several times?
You only have a few attempts to test out of a skill. Once you use all those attempts you lose the option
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.
Are you clicking where it says 'test out of skill'? You will still be able to do the lessons, but you won't be able to take a shortcut and test out of them. You should have the option to test out of skills again once you are higher up in your tree.