死心 (sǐ xīn): To give up hope / to be reconciled to death (Verb) — Meaning & Stroke Order

He couldn't find the key, so he gave up.

Do you still not give up hope and intend to continue investing in this doomed-to-fail project?

He did not give up hope because of temporary setbacks; instead, he became even more determined.

Seeing the other person's indifferent attitude, he completely gave up hope.

Only after receiving the explicit rejection letter did she completely give up hope and no longer harbor any illusions.