According to Concise Oxford English Dictionary, one says “never say die … to encourage someone not to give up hope”. It functions literally as a reply to a statement such as “we are all going to die”, expressing hopelessness in the face of a deadly situation.
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.