I assess the counter-argument the person presents, and if it is not consistent with my perception of logic and reason I dismiss it and announce myself the winner. If they end up agreeing with me this is a bonus. Whether or not they repeat the same argument, or back out of the argument, is irrelevant. I have found myself doing the same when the person I am arguing with is so fantastically stupid and set in their ways that the argument cannot continue because their entire premise is unreasonable or unverifiable. Your argument is not validated simply because your opponent is non-confrontational or has difficulty articulating certain complex concepts the moment you demand that they do.