MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) measurements taken during passes over Mercury's dayside hemisphere indicate that on four occasions the spacecraft remained in the magnetosheath even though it reached altitudes below 300 km. During these disappearing dayside magnetosphere (DDM) events, the spacecraft did not encounter the magnetopause until it was at very high magnetic latitudes, ~66 to 80°. These DDM events stand out with respect to their extremely high solar wind dynamic pressures, Psw ~140 to 290 nPa, and intense southward magnetic fields, Bz ~ −100 to −400 nT, measured in the magnetosheath. In addition, the bow shock was observed very close to the surface during these events with a subsolar altitude of ~1,200 km. It is suggested that DDM events, which are closely associated with coronal mass ejections, are due to solar wind compression and/or reconnection‐driven erosion of the dayside magnetosphere. The very low altitude of the bow shock during these events strongly suggests that the solar wind impacts much of Mercury's sunlit hemisphere during these events. More study of these disappearing dayside events is required, but it is likely that solar wind sputtering of neutrals from the surface into the exosphere maximizes during these intervals.