Carbon fiber is chemically stable, corrosion-resistant, and won't rust. That's why it works well in harsh environments. But strong oxidizing agents, such as hydrogen peroxide or sulfuric acid, may affect it.
Likewise, epoxy resin is inert and won't rust or corrode. It is sensitive to sunlight, though. So, cover carbon fiber composites with a UV resistant finish to prevent long-term damage from sunlight.
It's worth noting that carbon fiber composites may cause galvanic corrosion when in contact with some metals. While it won't lead to evident surface corrosion in the short-term, corrosion products add up and lead to damage with time. Fortunately, this needs specific conditions, and some coatings offer protection.
The short answer is yes. Any material can fail, but it's a bit more complicated than that. Many factors, such as the production process, design, and use, affects durability.
For instance, gaps can form, and it's more likely to crack if the manufacturer applies resin unevenly or doesn't use enough. Over time, these small cracks can spread until it breaks. Even minor impacts can eventually lead to failure.
The orientation of the fibers and the fiber layers also has a significant effect on fatigue resistance. As does the type of force you apply. Compression, shear, and tension forces cause different types of failure.
The woven fiber in a 0° layup has less torsional strength than at 45°, for example. So it may break if you twist it.