Neutron monitors are among the most robust and reliable detectors of GeV cosmic rays and aresensitive, with high precision, to modulations in Galactic Cosmic Rays (GCR). Hence, they canbe deployed for extended periods of time, decades, and are able to observe the modulation of GCRover many solar cycles. The South Pole Neutron Monitor, located at the geographic South Pole,which is both high latitude and high altitude, has an atmospheric cutoff of around 0.1 GV. In thefirst four decades of its operation, a secular decline in the neutron rates have been observed. Thedecline may have leveled off recently. Environmental effects, including snow build up around thehousing platform and the emergence and relocation of structures at the South Pole have been ruledout as causes of the decline. A recent study challenged the assumption that geomagnetic effectscan be ignored at the South Pole, in particular for cosmic rays approaching from select regions inazimuth and at large zenith angles. This work confirms that ignoring geomagnetic cutoff effectscould be important for the South Pole Neutron Monitor rates. We extend the investigation toinclude particle propagation in the Polar atmosphere, and the evolution of cosmic ray cutoffs atthe South Pole over several decades. A connection is made between the evolving cutoffs and thedecline in neutron monitor rates.