We extend the truncated three wave theory used to describe degenerate four-wave mixing in optical fibers to take into account the impact of higher order harmonic sidebands. Using second order perturbation theory combined with adiabatic elimination, our extended theory preserves the initial framework of three waves description. This allows the subsequent discussion regarding the origin of the non-preservation of Fermi-Pasta-Ulam-Tsingou recurrence. Our analytical results are supported by numerical simulations and experimental observations.