" Never say die!" has three meanings.
First, it means " Don't give up!" to encourage you to continue doing something hard.
Eg: Mary: I'm fed up with this homework. It's driving me nuts. I think I can't finish it in time.
Jane: Come on, Mary. Never say die!
Sencond, it shows something that you say which means that you should not accept that you have failed while there is still a chance that you may succeed.
Eg: You still have enough time to handle this problem. Never say...