The phrase "beat a dead horse" means to pursue a pointless or unproductive argument or line of discussion. However, there are many alternative expressions that convey this same idea. For example, one could say "flog a dead horse," "run into a brick wall," "bang one's head against a wall," "push the envelope too far," "spin one's wheels," or "tread water." All of these alternatives help to illustrate the idea of wasting time and energy on something that is unlikely to produce any positive results. Whatever phrase one chooses to use, the fundamental message remains the same: it's time to move on from an unproductive discussion.