fight a losing battle
Definition from Wiktionary, the free dictionary
- To continue to wage war when it is clear that one is not going to win.
- (idiomatic) To try to do something so difficult that it will probably end in failure.
1984, Lucy Gore, Diary Of A Working Mum, page 18:
- The bus was oppressively warm and the air-conditioning was fighting a losing battle with the heat.