Degradation in carbon fiber typically comes from bond loss between the fibers and the resin due to degradation of the resin itself, including cracks and fissures. The two things most likely to accelerate that are a) acid attack (which is the primary concern regarding its use in civil structures, just as it is for steels), and b) a combination of UV and moisture (the two play off one another and accelerate degradation). In the conditions a typical firearms barrel would see (stored indoors, water contact only, wiped down after use), they will likely last a very, very long time. Even then, "failure" of the carbon fiber is likely to only be some loss in tensile strength of the matrix, which depending on thickness, length of the barrel, may or may not even affect accuracy. There are also mitigating measures that could be done, such as intermittent application of UV protectant clear coats or ceramics.
TLDR - You will probably shoot the barrel out before it ages out of use, IMO.
