An analysis of the influence of the magnetic field of an intense, high-freq
uency laser pulse on the stabilization of an atomic system is presented. We
demonstrate that at relatively modest intensities the magnetic field can s
ignificantly alter the dynamics of the system. In particular, a breakdown o
f stabilization occurs, thereby restricting the intensity regime in which t
he atom is relatively stable against ionization. Counterpropagating pulses
do not negate the detrimental effects of the magnetic field. We compare our
quantum mechanical results with classical Monte Carlo simulations.