Different nearly constant loss phenomena are investigated in borate glasses with compositions xNa₂O·(1−x)B₂O₃, for 0 ≤x≤ 0.3. The ionic conductivities caused by these effects are studied in wide ranges of temperature and frequency, spanning 4.3 K to 573 K and 100 mHz to 1 MHz, respectively. In a first step, we show how to identify the nearly constant loss (NCL) in 0.3Na₂O·0.7B₂O₃ glass. In the procedure, the scaling property of the conductivity caused by ordinary hopping is used to remove this component from the total conductivity as measured as a function of temperature at fixed frequency. The resulting NCL component is seen to be proportional to frequency and to display no temperature dependence. In a second step, a broad-band relaxation process is shown to exist in amorphous boron oxide and in sodium borate glasses with x≤ 0.1. It is most probably due to the presence of traces of water, with hydrogen ions behaving as reorienting and interacting local dipoles. In a third step, we propose a simple formal treatment of the NCL phenomenon, tracing it back to a large number of interacting ions, each of them moving locally. The key aspect is a “see-saw-type” time dependence of their individual single-particle double-well potentials, which is due to their Coulomb interactions. The individual ion does, therefore, not require thermal activation and is thus kept in motion even at cryogenic temperatures.