I have a mapcase made of clear plastic (PVC I think). It has a roll top held shut with velcro. Both sides of the velcro were attached by some sort of welding process but one of them has completely come off. I've tried reattaching it with hot glue, which seemed OK at first, but didn't survive one use. I've tried pressing the plastic to the backing of the velcro with a heated tool, but despite the hot plastic smell there was no adhesion.

Not only is it my most waterproof mapcase, ideal for inkjet-printed maps in the rain, but it attaches to the handlebar bag of my bike. Replacements don't seem to be available, and it's perfect for riding to a hike, something I quite like to do. But with the velcro missing the maps simply fall out (it's at the bottom).

I don't want to sew through the plastic unless I absolutely have to: it will breach the waterproof section, and I don't appear to have anything that I could use to seal the holes.

On the left, a strip of velcro that's firmly attached; In the middle, the remains of the weld; on the right, the velcro that came off. The weld (which shows up as a white rectangle) is textured in the side that touched the velcro, and smooth on the other side, suggesting that any melting was very controlled, and possibly delivered through the velcro (which has an edge of just fabric).