ようになる

Tobira states that ようになる is used to "indicate a gradual change over a certain period of time." It essentially expresses the idea that someone has come to the point where they do (or can do) something, or don't (or cannot) do something. This grammar is often used with the potential form of verbs.

Verb + ないようになる is pretty similar to Verb + なくなる, except the former expresses a more gradual change over a period of time. It must be used with the plain form of a non-past verb.

日本人の友達ができてから、日本語が上手に話せるのようになった。
Since I've made a Japanese friend, I've come to be able to speak Japanese well.

息子を養ってから、寝れないことに慣れるようになった。
Since I adopted my son, I've gotten used to not being able to sleep.

父は病気になってから、お酒を飲まないようになった。
Since my dad got sick, he's gotten to the point where he's stopped drinking.

この子は赤ちゃんのころはよく泣いていたが、４歳になって、あまり泣かないようになった。
When this kid was a baby he cried all the time, but since he turned 4, he's gotten to where he doesn't cry very much anymore.