The polarized (VV) and depolarized (VH) light scattering spectra of polyisobutylene, poly(methyl methacrylate), and glycerol were measured in the gigahertz frequency range at temperatures below and above the glass transition. Both VV and VH spectra exhibit a significant constant loss contribution that appears as a frequency-independent imaginary part of the susceptibility spectrum. Existence of the frequency-independent susceptibility in VV spectra below the Brillouin lines suggests that the constant loss also appears in mechanical relaxation in the gigahertz frequency range. Intensity of the constant loss increases strongly with temperature. Analysis of the spectra and literature data suggests that the constant loss can be general for many glass-forming systems, but it is hidden in many cases by other relaxation contributions.