I think the problem is that JWs and MORMONs are both taught that the RIGHT candidate will have the RIGHT heart condition and will just LISTEN and NOT debate...so when debate begins, they KNOW they have found a dead end and its time to move on.
Yeah I've heard and was taught this when out in field service that whenever someone wanted to argue, just move on because they were "being used by satan" and were evil, and that you could be geting the message to somebody who would listen. That's why I do not even know how to approach my witnoid relatives because I know that there minds aren't even 'open' to debate because they have their whole mentality set into it. But then again who didn't?
It's difficult, but they aren't willing to listen mainly to those reasons listed above; they made up their minds about your argument before they have any real backing to discredit or counter it. You are just 'evil/wicked' and that is it.