That doesn't give up in despair; indomitable(adjective)
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Use "never-say-die" in a sentence
"Most days, it is my ragtag, never-say-die colleagues in foreclosure wonderful people and some non-bank-owned journalists who are willing to speak the truth about the bank documents used to steal homes."
"And perhaps that is why, even as their season sinks into irrelevance, Mets manager Terry Collins speaks on a near daily basis about his side's never-say-die attitude."
"The Imagineers pride themselves on their never-say-die spirit."