We investigate how the nonlinearity of the Zeeman shift for strong magnetic fields affects the dynamics of rf field induced evaporative cooling in magnetic traps. We demonstrate for the 87-Rb and 23-Na F=2 trapping states with wave packet simulations how the cooling stops when the rf field frequency goes below a certain limit (for the 85-Rb F=2 trapping state the problem does not appear). We examine the applicability of semiclassical models for the strong field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent $^{87}$Rb experiment [Phys. Rev. A 60, R1759 (1999)].