We theoretically consider photorefractive degenerate four–wave mixing oscillators and show that, for this particular system, the linear stability analysis technique leads to wrong results. The reason for that astonishing failure lies in the unphysical predictions of the undepleted pump approximation, which appears naturally during the linearization process of the full model. As a consequence, photorefractive four–wave mixing does not admit a perturbative treatment that permits the derivation of mean–field models, and one is forced to use the full model in order to make sensible predictions.