CF doesn't have a limitless ductile life, and neither does the (usually) epoxy matrix. The mechanism of age related failure differs somewhat due to the amorphous nature of the matrix and its lacking crystalline structure, but ultimately it does have both a fatigue limit and fatigue life.
They are also affected adversely by many nasties from natural stuff like UV and chemicals in salty sea air, through to artificial bits in the environment like the deodourant in your sweat.
It's a greater material, and with good design and thoughtful construction is brilliant. But it not a wonder material and shouldn't be regarded as impervious, indestructible or immortal, but with care and consideration is liable have a useful lifespan measured in decades.