The standard tunneling model describes quite satisfactorily the properties of amorphous solids at temperatures T < 1K in terms of an ensemble of two-level systems including the logarithmic temperature dependence of the dielectric constant. Yet, experiments have shown that at ultralow temperatures T< 5 mK such a temperature behavior breaks down and the dielectric constant becomes temperature independent (plateau effect). In this Letter we suggest an explanation of this behavior exploiting the effect of the nuclear quadrupole interaction on tunneling. We also predict that the application of a sufficiently large magnetic field B> 10T should restore the logarithmic dependence because of the suppression of the nuclear quadrupole interaction.