We have investigated the crossover in the ac conductivity of ionic conductors from the linear frequency dependence (near-constant loss) found at low temperatures, to the power law dependence characteristic of ionic hopping at higher temperatures. We have analyzed electrical conductivity measurements of the fast ionic conductor Li0.18La0.61TiO3 in the frequency range 20 Hz–5 MHz, and from room temperature down to 8 K. Our results show the failure of the so-called `augmented Jonscher's expression' to describe the ac conductivity in the whole frequency and temperature ranges, and give further support to the origin of the near-constant loss in the vibrational relaxation of ions within their cages.