It has been known that (untrapped) ring current particles can be lost through the dayside magnetopause into the magnetosheath, which is regarded as one of the major mechanisms contributing to the ring current decay. In this paper, we suggest that the solar wind dynamic pressure can play a significant role in the dayside loss in a new aspect. In order to show that, we have first analyzed the average characteristics of the dynamic pressure based on 95 geomagnetic storm events selected from the period 1997--2002. We find that the dynamic pressure overall enhances during the magnetic storm. The enhancement is most significant during the storm main phase compared to the prestorm and recovery phases, and it is higher for stronger storms. Using one of the most recent Tsyganenko models, T01s, we show that this enhanced dynamic pressure that pushes the magnetopause to move inward leads to a reduction of the scale length of the gradient of the magnetic field magnitude along the magnetopause. This results in the enhancement of the magnetic drift speed across the magnetopause. On the basis of the test particle orbit calculation, we explicitly show that this effect can be a significant factor for the particles to effectively cross the magnetopause. It applies to the adiabatic particles that have a relatively small gyroradius near the magnetopause compared to the magnetopause thickness. These particles cross the magnetopause by some number of the magnetic gradient drift motion, being in contrast to the particles with a relatively large gyroradius that can enter into the magnetosheath by crossing the magnetopause with less than one gyromotion. We argue that this can often apply to a substantial population of the ring current particles.