From Longman Dictionary of Contemporary Englishback down phrasal verbLOSE A GAME, COMPETITION, OR WARACCEPTto admit that you are wrong or that you have lost an argument Both sides have refused to back down. → back→ See Verb table
Examples from the Corpus
back down• Even though it was obvious Emma's demands were unrealistic, she wouldn't back down.• Congress has backed down on its demand for an increase in defense spending. 