Why does a tragic hero usually fail or die in a Shakespearean tragedy?

Answer 1

Shakespeare's tragedies invariably end with the deaths not only of the main character or characters but usually a bunch of others. Timon of Athens is probably the least bloody--Timon is the only one who dies. Coriolanus is likewise fairly restrained, but Coriolanus of course dies at the end (there are a lot of bloody battle scenes in the middle though). The body count in Hamlet, King Lear and Titus Andronicus is through the roof. (In Hamlet, not only does Hamlet die, but so does his mother, and his stepfather, and his girlfriend, and her father and brother, and two of Hamlet's schoolfriends. In Titus, Titus dies and so do three of his sons and his daughter and his son-in-law, plus the Emperor and the Empress and three of her sons. In Lear, Lear dies together with all three of his daughters, one of his sons-in-law, plus the Duke of Gloucester and one of his sons, sundry soldiers and in all probability Lear's Fool)

Answer 2

That it's in the very definition of 'tragic hero' is the reason why such a character fails or dies in a Shakespearean tragedy. The adjective 'tragic' refers to an unhappy, unfortunate end or outcome. The noun 'hero' refers to a character who does great deeds. When the two come together, the consequence is a character who's inspirational in act, but unenviable in fate or in apparently free will choices and actions.