More on Throw Up the Sponge from Infoplease:

• Throw Up the Sponge - Throw Up the Sponge (To). (See Sponge.) Source: Dictionary of Phrase and Fable, E. Cobham Brewer, ...
• Sponge - Sponge Throw up the sponge. Give up; confess oneself beaten. The metaphor is from boxing matches. ...
• Cry Cave - Cry Cave To). To ask mercy; to throw up the sponge; to confess oneself beaten. (Latin, caveo.) (See ...
• Dictionary of Phrase and Fable: T - Definitions, origins, and illustrative excerpts for words, phases, and literary allusions starting with "T"