Have you tried sitting her down and talking to her about this? I'm not necessarily talking about the "it's wrong for you to try to manipulate people" talk, although that *might* work. But maybe you could sit down with her and explain a little about basic logic and logical fallacies. There's plenty of stuff out there to read on the nature of logic and how to construct logical arguments (ugh...bad memories of college philosophy here). Help her understand how to use logic properly and how to construct truly convincing FACTUAL arguments. Make her understand that REAL logical arguments are going to get her much further than attempts to manipulate you. Of course, I'm assuming that if she WERE to out-logic you, properly, without emotional manipulation, you would admit it and change your position.
