You've met her 3 times in your life. Over several months. And haven't seen each other in 6 weeks. You haven't mentioned how often you communicate by phone or webcam, so I am going to jump to conclusions and assume that your telecommunication relationship is nothing to shout about.
From that, my conclusion is:
You're NOT in a long distance relationship. Heck, you're not in a relationship.
In fact, I'd put it down as somewhere between acquaintances and friends from what I've read so far.
Not that I'm saying that you can't FORM a long distance relationship. It sounds like it'd take work and effort on your part though, which neither you or the girl sound enthusiastic about.
The fact that you're talking about the relationship dying, when it hasn't even begun, probably has a lot to do with it. Let's be honest, you're not really THAT interested, are you? And I bet, neither is she.
You happened to meet each other, felt some attraction, had a good time... but that's as far as it went, for now. Why don't you chill out, go with the flow, see if there's anything deeper there as you go along... no pressure man.