No, you've lost the argument when you've failed to make your point. I don't believe that to be the case here. "Reductio ad Hitlerium" isn't a real logical fallacy, it's just a joke someone made up and we've allowed to perpetuate.
You misunderstand the purpose of logical fallacies. They do not indicate when someone has lost the argument. In fact, the belief that this is the case is itself a logical fallacy.
