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To persist in fighting. The two players fought on until a referee was finally able to get in between them and break it up.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
to continue to fight. The boys fought on until one of them was down. They fought on until they were exhausted.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.