I only perused the articles quickly, but I believe you misconstrued them. The first one did relate to fatigue with use, but did not specify what fatigue means. I assume breakage. And there is no description of the mechanical properties right up to the catastrophic failure. The test was how many cycles could the test specimen withstand at each amount of bending force per unit area (stress) before "failing". Now OP is not asking about catastrophic failure, but rather about stiffness after many stress cycles but prior to breakage. The article does not address that question. It isn't mentioned at all.

In fact it would not be surprising if the shoe sole actually became stiffer as it approached the fatigue limit as the bending is really a form of "cold working" of the material. It is not altogether outlandish to think that the nylon crystallinity would be increasing over time as the material is bent back and forth.

Actually then, the answer to OP's question may be, "Yes, cycling shoes have a useful lifetime," if you define lifetime as the interval up to catastrophic breakage of the sole due to fatigue. I have never heard of that happening, however. So the point is moot.

The second article isn't about repetitious flexing at all, but rather about the effects of heat and moisture on the mechanical properties of glass-reinforced nylon. That does include flexural stiffness, but has nothing to do with changes in properties with use. The effects of temperature and humidity on nylon are instantaneous. They have nothing to do with age. And in the conclusions the authors make clear that the effects are reversible with changes in environmental conditions which occur all the time. So this article is also irrelevant to the OP's question. But it is interesting that on a hot, 99% humidity day any nylon-soled cycling shoe could feel noticeable less stiff than on a dry, cold day.