We show that substantially enhanced mass-loss at periastron passages, as is expected in the grazing envelope evolution (GEE), can compensate for the circularization effect of the tidal interaction in binary systems composed of an asymptotic giant branch (AGB) star and a main sequence secondary star. By numerically integrating the equations of motion we show that under our assumptions, the binary system can maintain its high eccentricity as the AGB star evolves towards the post-AGB phase. Our results can explain the high eccentricity of some post-AGB intermediate binaries (post-AGBIBs), i.e. those with an orbital periods in the range of several months to few years. In the framework of the GEE, the extra energy to sustain a high mass-loss rate comes from the accretion of mass from the giant envelope or its slow wind onto a more compact secondary star. The secondary star energizes the outflow from the AGB outer envelope by launching jets from the accretion disc.