Your mesh has some elements with a rather high aspect ration in the middle - if stress gradients are large there and you use linear elements, your results will not be reliable.
If you chose reduced integration elements as in the model, there is some danger of hourglassing depending on how the model is loaded; you should carefully check for that. (If you switch to fully integrated, be aware of shear locking instead.)
What exactly is the question regarding fatigue? Is it HCF or LCF? Do you want to simulate full cycles or use cyclic stress-strain curves? Or do you want to apply a Paris law by calculating the stress intensity factors around the cracks you seem to have in your structure?