You just got the phone in June and they are unwilling to replace it? That doesn't sound like the Apple Store that I'm used to dealing with. I'd try again. Did you contact Apple upon noticing the damage initially?
I haven't experienced any problems with mine. If Apple is not willing to replace yours after the 3rd one, I'm thinking there might be more to this story. I have never known Apple to not replace one of their products that is faulty no matter how many times they've done it.
The only problem I have once in a while is with my Mophie case. Tells me that "the accessory is not compatible with this device" or something like that. Other than that, which is not a big deal, nothing.