Instruments on the Pioneer Venus Orbiter have detected a substantial ionosphere on the nightside of Venus during most orbits. However, during some orbits the nightside ionosphere seems to have almost disappeared, existing only as irregular patches of low-density plasma. The solar wind dynamic pressure on these occasions is greater than average. We have correlated data from several instruments (Langmuir probe, ion mass spectrometer, retarding potential analyzer, magnetometer, and plasma analyzer) for a number of orbits during which the nightside ionosphere had disappeared. The magnetic field tends to be coherent, horizontal, and larger than usual, and the electron and ion temperatures are much larger than they usually are on the nightside. We suggest mechanisms which might explain the reasons for the disappearance of the ionosphere when the solar wind dynamic pressure is large.