can't or couldn't?

I'd use couldn't. The inability is a past-time situation.

I am glad to know your answer:-) My textbook says otherwise and I disagree with that:-) I really appreciate your help:-)

I don't know what your book says, but if it claims that 'It happens that you can suddenly do something that you can't' is good English, then it is misleading you.

Having said that, I have to admit that I can imagine native speakers saying it in informal conversation. It makes no sense logically, but we don't always think of logic when we are chatting with friends.

I see. The same goes for when we speak Japanese. We have a habit of "intentionally" twisting grammar rules we supposedly learned back in school. It's a fun part of language when you become fluent enough in that language.

What's great about this forum is that many of the native speakers here actually know the difference between formal and casual English and explain it in excellent ways