We investigate numerically the time variations of geomagnetic cutoffs of solar energetic particles. As a test case, the geomagnetic cutoff of 25 MeV protons is modeled for the 23--24 November 2001 solar energetic particle (SEP) event. Following Smart and Shea <2001>, solar energetic particle access is determined by computing the reverse particle trajectories. Magnetospheric fields are obtained from the Lyon-Feder-Mobarry (LFM) global MHD model, which is driven by measured solar wind parameters at the sunward boundary. We find well-defined surfaces of constant cutoff that exhibit dynamic behavior in response to solar wind conditions. We show that dynamic modeling of cutoff surfaces may be used as a tool to investigate SEP access to the inner magnetosphere. The numerical results are compared with proton observations from a highly elliptical orbit (HEO) satellite. The results suggest that an enhancement in the solar wind dynamic pressure plays a role in the observed ion injection.