Sounds like it might have been something with that specific fiberglass piece. The molded plastic and carbon fiber finished with a clean resin usually adheres very well. If the underside mounting points are rough then the double-sided tape probably won't work.
Just as another example, many of the heavy plastic body side moldings on older Pontiacs and even a lot of Chrysler products used a lot of 3M double-sided tape from the factory, often combined with a few trim clips. If it's good enough for original equipment manufactured (OEM) use, it's probably good enough for aftermarket use, but will depend on the surface prep of what you're trying to attach.
Eric H. - '04 Neon SRT-4 (eBlue/S2) - '92 Dodge Daytona IROC R/T
'91 Dodge Spirit R/T - '19 Pacifica Hybrid Limited - '14 CTS-V Wagon
'08 Cobalt SS Turbo - '14 Cruze Turbo Diesel - '02 SVT Focus (S/C)
'04 SVT Focus (EAP) - '07 Ram 1500 - '81 & '85 Chevy Citation X-11
'90 Pontiac Turbo Gran Prix (ASC/McLaren) - '93 Olds Achieva SCX W41