Fatigue from worst to best: aluminum, steel, titanium, carbon/epoxy. Carbon parts have to be painted, or clear coated with a clearcoat that absorbs UV, because epoxy does degrade from UV exposure, and could degrade from exposure to nasty stuff in the atmosphere, like pollutants produced by a race car. Ferrari presumably doesn't paint their carbon undercarriage parts.
I would have to disagree about steel being the second worst on fatigue resistant. If the manufactur uses the correct steel the Endurance limit of the steel would be higher the the maximum amount of stress the steel would experience. In other word, steel has a certain graph that says if the stress is below this line the steel won't crack under equilibrium conditions. The graph, should you want to look it up, is called a stress number of cycles to failure curve (S-N curve). That being said if the manufactur uses the correct steel the steel frame should never break. That would sound very fatigue resistant to me and should be at the top of the list. However, scratches and other defects in materials will weaken any material and has an effect on how the material reacts. I can't comment on titanium because I haven't learned that subject.