We present a series of experiments, in which the relativistic (5-20 MeV), low current (tens of milliamperes) electron beam from a microwave (2856 MHz) linear accelerator interacts with an air-filled cylindrical cavity whose pressure was varied from 1 µTorr to 100 torr. The pulsed structure of the electron beam drives an electromagnetic resonance in the cavity, but the magnitude of this resonant signal was seen to collapse on a time scale depending on cavity pressure. This is believed to be due to beam-driven generation of conductive plasma inside the cavity, which detunes the center frequency the of cavity mode the beam drives. The resonance collapse generally occurred on a 10-1000-ns time scale and exhibited a complex, nonmonotonic dependence on cavity pressure. Four distinct pressure regimes were exhibited: 1) at very low pressures, no collapse occurred; 2) at low pressures, a field-ionization-driven collapse occurred; 3) at moderate pressures, a combination of field and collisional ionization drove the collapse; and 4) at high pressures, collisional ionization dominated the collapse. These pressure bounds are generally highly dependent on beam and cavity parameters. This work broadly demonstrates that not only can an electron beam drive a resonant interaction in a radio frequency (RF) structure, but it can also generate a plasma inside of the structure that alters the nature of the interaction, potentially by an order of magnitude or more.