We report on the temperature and mass dependence of the nearly constant loss (NCL) in several ionically conducting materials, both crystalline (Li0.18 La0.61 TiO3 and (Y2O3)0.16 (ZrO2)0.84) and glassy (M2O·3B2O3, M=Li, Na, K and Rb). The magnitude A of the NCL is found to be larger for those materials showing higher dc conductivity values at room temperature, and shows weak temperature dependence of the form A∝exp(bT) in all cases. We have also found that A systematically decreases upon increasing the mass of the mobile alkali ion in the borate glasses. All these results point to the relaxation of ions in a very slowly decaying cage as the origin of the NCL.