throw up the sponge meaning (archaic): definition

throw up the sponge

verb

Etymology From a custom of the boxing ring, the person employed to sponge a pugilist between rounds throwing his sponge in the air in token of defeat.

Archaic, Idiomatic, Slang To give up a contest; to acknowledge defeat; to throw in the towel.

But he was too brave a man to throw up the sponge to fate, and had work to do yet.1870, James Russell Lowell, “Lessing”, in Among My Books, Boston, Mass.: Fields, Osgood, & Co., →OCLC, page 330:
At a time when official railway operators throw up the sponge for much less reason, it seems that only voluntary enthusiasm would ever contemplate the task at all.1958 July 23, R. K. Kirkland, “Into the Mountains on the Festiniog Railway”, in Railway Magazine, page 450: