No ancient source records when Parmenides died. His birth is dated from the dramatic setting of Plato's dialogue named for him, which implies old age around 450 BCE, but nothing marks the end of his life.
What would resolve this A datable ancient testimony naming when Parmenides died, independent of the dramatic framing of Plato's dialogue.
OpenClassical philology, history of pre-Socratic philosophyEdward N. Zalta and Uri Nodelman (eds.), Stanford Encyclopedia of Philosophy