give up on (someone or something)
idiomDefinition of give up on (someone or something)
1
: to stop trying to improve the condition of (someone)
He has gotten in trouble many times, but his parents have never given up on him. Please don't give up on me. I promise I'll do better.
2
: to stop having hope of seeing (someone)
We'd given up on you hours ago!
3
: to stop trying to do or achieve (something)
They have given up on their plan to build a new factory. She hasn't given up on trying to convince her husband to buy a new car.