dać za wygraną Englisch:

once he’s made up his mind he’ll never back down

Faced with opposition to his proposal, he had to back down.

Sheila was right, so Paul had to back down.

They often have terrible rows because they both refuse to back down.

Local residents have forced the local council to back down from/on its plans to build a nightclub on their street.

Although the chance to win this round was smaller and smaller, Ania didn't back down.

both lawyers refused to back down

We are not going to back down on our position.