Don't you always use "失敗"? "挫折" is a noun that means "to experience failure". It is used when describing situations in which you give up/fail something, you're not motivated, or you're frustrated because you cannot achieve what you want.
"失敗" is only used when you fail something, but "挫折" is also used when you're not motivated even if you don't fail yet.
Ken and Leo are catching up.
- Ken: How is your Cantonese study going?
広東語の勉強はどう？ - Leo: I've just started learning the basic grammar. I do study a little every night.
基本的な文法を学び始めたばかり。毎晩少し勉強している。 - Ken: Great. I don't last in doing almost anything.
すごい。私なんて、何やっても続かないよ。 - Leo: Me neither. I always get discouraged, but I'm really going to try this time.
私もだよ。いつも挫折するけど、今回は本気で頑張ってみようと思って。
Amy's boyfriend is a professional soccer player and he broke his right leg.
- Jim: I'm thinking of retirement from soccer. I don't feel like my leg will get better.
(サッカーを)引退しようと思っている。脚が良くなる気がしない(*)。 - Amy: Are you serious? I think it's much better now. Why?
本気なの？だいぶ良くなっているじゃん。なのに、なんで？ - Jim: I've seen many players fall by the wayside due to injury. It's time for me to quit soccer.
俺は、多くの選手が怪我で挫折するのを見てきたんだ。辞める時なんだよ。
*～な気がする means to feel like. It's a common phrase.