Frankly wrote:
If I can't get them to fix it, wouldn't it be better to cut a small slit in the membrane, fix the screw/nail, and then patch with eternabond? Otherwise it looks like the screw/nail could puncture both the membrane and the tape? Or are you thinking this will void the warranty?
True whatever it is could push through both the roof and the eternabond, but I'll bet it's more likely that it won't even penetrate the roof.
If I was real concerned I would slice open just enough to deal with the screw which might mean just removing it and then patch it with a square of Eternabond. If you clean the area well with Acetone and then push the Eternabond down really tightly to squish it, it will probably outlast the camper.
A few years ago my Walmart carried small patches of Eternabond tape in the RV aisle, you might check at yours. It's a bit more per foot that way, but if you only need a few inches it's a much better deal than a whole $50 roll of 50 feet.