For the first time in his life, he gave up hope.
By now I had given up hope for our plan.
Everyone in my family had also given up hope by now.
With a little group of people who didn't give up hope.
He'd just about given up hope when he found them.
He'd been in the water two days and given up hope.
By now, they might well have given up hope of being found.
They did not give up hope for almost two hours.
He'd given up hope of having her leave with them.
But he wanted to believe them, could not give up hope.
Idiome