시들해지다 (si-deu-rae-ji-da) – to wane/wear off/fade
You realise that there is a “지다” at the end of this word, which has the meaning of “to become”.
시들다 by itself means “to wither (away)” or “to slowly die off”.
Therefore, we can look at 시들해지다 to be a word to emphasise on the fact that it was a lot better before but has now became worse.
In a way, 시들다 is enough to express how something is slowly “withering away” but we can use 시들해지다 to emphasise on the fact that something is in a much worse state than before.
Examples:
사람들이 사랑은 세월 따라 다 변하고 사랑하는 사람한테 관심이 천천히 시들해질 거라고 생각한다.
People thinks that love will all change as time flies and the concern for a person one loves will slowlywither away.
성공을 얻도록 모든 하고 싶은 일과 해야 하는 일들을 열심히 해야 하며 열정이 절대 시들해지지 마라.
To succeed, one needs to work hard for the things you want to do and the things you should do while never allowing your passion to wane.