dead horse, to beat/flog a

To pursue a futile goal or belabor a point to no end. That this sort of behavior makes no sense was pointed out by the Roman playwright Plautus in 195 B.C. The analogy certainly seems ludicrous; what coachman or driver would actually take a whip to a dead animal? The figurative meaning has been applied for centuries as well; often it is used in politics, concerning an issue that is of little interest to voters. However, some writers, John Ciardi among them, cite a quite different source for the cliché. In the late eighteenth century British merchant seamen often were paid in advance, at the time they were hired. Many would
spend this sum, called a dead horse, before the ship sailed. They then could
draw no more pay until they had worked off the amount of the advance, or
until “the dead horse was flogged.”