We performed a statistical study of downward moving protons and alpha particles of ~keV energy (assumed to be of solar wind origin) inside the Martian induced magnetosphere from July 2006 to July 2010. Ion and electron data are from the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) package on board Mars Express. We investigated the solar wind ion entry into the ionosphere, excluding intervals of low-altitude magnetosheath encounters. The study compares periods of quiet solar wind conditions and periods of solar wind pressure pulses, including interplanetary coronal mass ejections and corotating interaction regions. The solar wind ion precipitation appears localized and/or intermittent, consistent with previous measurements. Precipitation events are less frequent, and the precipitating fluxes do not increase during pressure pulse encounters. During pressure pulses, the occurrence frequency of observed proton precipitation events is reduced by a factor of ~3, and for He^2+ events the occurrence frequency is reduced by a factor of ~2. One explanation is that during pressure pulse periods, the mass loading of the solar wind plasma increases due to a deeper penetration of the interplanetary magnetic flux tubes into the ionosphere. The associated decrease of the solar wind speed thus increases the pileup of the interplanetary magnetic field on the dayside of the planet. The magnetic barrier becomes thicker in terms of solar wind ion gyroradii, causing the observed reduction of H^+/He^2+ precipitations.