Did you get the mounting gear with it when you bought it?
I'm told my many people that the suction cup won't fall off in flight but I don't trust it. You might get to 8,000ft, come down again and be less 1 go-pro.
I have seen people use the mount that comes with it but have drilled a hole in the factory bracket and mounted it on an existing airframe screw, eg like the ones that hold on the wing-tips. Seem to work well. If you don't have that luxury, perhaps some duct tape but make sure you don't take the paint off with your 100mph tape if you are hiring someone else's aircraft.