We still haven't given up hope of finding her alive. 我们还没有放弃她生还的希望。
He just believed in her and no matter how bad things got, he refused to give up hope.
I know the situation is dire, but don't give up hope.
I'd started to give up hope that I'd hear back from them.
We never gave up hope that he would come back home.
See also: give up something