Temperature dependence of magnetic characteristics of Fe and Fe-Ni invar is considered in the dynamic nonlocal approximation of the spin-fluctuation theory. Numerical calculations show that the magnetic characteristics can have a discontinuous jump at high temperatures, well below the Curie temperature. Using methods of the catastrophe theory, we investigate the effect of small changes in the initial data on the results of the calculation. It is demonstrated that the discontinuous jump can only be smoothed but cannot be eliminated entirely without a significant change in the system of equations of the spin-fluctuation theory. Possible variants of such changes are discussed.