The reason why your friend is acting that way is because JWs are driven by appearances, in reality they are more concerned about how to behave than what's in the heart. This, of course, is backwards if you ask anyone with common sense about love, relationships, spirituality etc. The sad thing is they will go against their instincts because of what they've been told, which is why most people believe they need to reason with their unreasonable thinking, since that is the dominant force that is controlling them. However, even if she doesn't understand it on a conscious level, if you really care for her and show it in different ways (and it can't help but show) it will have an impact. I guess the question is just what the relationship is to you and to her. I make a distinction between what it IS and what it MEANS, because again the mind is playing tricks on someone like this, and she is more likely to interpret what something means, in this case sex outside of marriage, with a textbook answer from the way she was taught. I don't know how close you two are, but I have heard of prototypically witness girls that preaches full time and all that just drop it because they met someone. Of course, it is possible that some of them just wants to have sex, but if they're not getting love from people in the witness community - including their own family members, but IS getting it from a "worldly guy", they'd have to really hurt themselves to turn away from the one who does love them.
One of the guys that facilitates this local XJW support group was saying a lot of people just end up leaving because they get tired, not because they have a particular issue with the teachings and such. Sometimes it gets to the point where you really hit bottom, but then if someone's there to support you as a human being, it's only natural that you'll welcome it. The thing is it could very well be that the witness has a chance to go back to their witness family too, and in that case they may mistaken the conditional love for the real thing, just because it sounds like a good deal. Though ultimately it will be up to her, people know when someone really loves them - even if they don't know what it is, they know there's something significant going on. For your part don't over extend too much and drive yourself crazy. All you can do is give her a chance, the rest is up to her.