To throw up the sponge Meaning, Definition & Usage

Definitions
  1. to give up a contest; to acknowledge defeat; from a custom of the prize ring, the person employed to sponge a pugilist between rounds throwing his sponge in the air in token of defeat. Cant or Slang "He was too brave a man to throw up the sponge to fate." Lowell. now, through in the towel is more common, and has the same origin and meaning.

Webster 1913