The conservation of spectral asymmetry is a fundamental feature of the ideal four-wave mixing process as it exists in a medium combining quadratic chromatic dispersion and third-order nonlinearity. We test in this paper the robustness of this invariant in an experimental configuration where the excitation conditions of an optical fiber are sequentially updated, mimicking infinite propagation. This theoretical and experimental study reveals the high sensitivity of the asymmetry to very slight deviations from the ideal case, and we show that our idealized system behaves as an intermediate case between the ideal case of non-cascaded fourwave mixing and propagation in a system governed by the nonlinear Schrödinger equation.