なかなか〜ない
Just won't…, taking forever to…machine translation
Formationなかなか + verb ない-form / negative potential
なかなか + negative means "just won't…, still hasn't no matter how long you wait or how hard you try": バスがなかなか来ません (the bus just won't come), なかなか覚えられません (I just can't memorize it). This pattern carries the speaker's impatience: something that should have happened by now still hasn't.
なかなか pairs especially often with the negative potential form: なかなか眠れません (I just can't fall asleep), なかなか上手になりません (I just don't get any better).
Note that なかなか also has an AFFIRMATIVE use with adjectives, meaning "quite, considerably": この問題はなかなか難しい (this problem is quite hard), なかなかいいですね (that's pretty good). Look at whether what follows is affirmative or negative to tell the two meanings apart.
Examples
バスがなかなか来ません。
The bus just won't come.
日本語の発音がなかなか上手になりません。
My Japanese pronunciation just isn't improving.
この問題はなかなか難しいですね。
This problem is quite hard, isn't it?