Try E-6000, and give it a week to out-gas and cure.
Seriously tough glue once it dries. I use it on slope-soaring R/C sailplanes, and we found a plane that had been lost down the slope exposed to the elements for four years, 1200-odd days in the sun, and it held up great. The glue was still clear, rubbery and flexible, and it wasn't even the UV-inhibited E-6000.
You'll find it at Lowes, or plumbing supply shops.