If you have a never-say-die attitude, you don't give up or get discouraged, no matter what. People love a never-say-die spirit because it describes people or teams that just don’t quit. Unless they die, then they can’t say it anymore.
A never-say-die soldier keeps on fighting even when the situation is scary and dangerous. Someone with a never-say-die attitude about winning a game will keep on playing hard even when they’re losing by a lot. You can also use this phrase to encourage someone who's feeling hopeless — a football coach might call to his struggling team, "Never-say-die!"