Poly(vinylpyrrolidone)-water solutions of 60-80 wt % PVP apparently do not freeze when cooled far below the expected freezing point. Such solutions remain highly viscous liquids and ultimately become glasses. It has been reported before that when small-angle X-ray scattering from these solutions is measured, occasionally very sharp peaks appear. The collection of those peaks, that have, in general, a short lifetime, constitutes a hexagonal planar reciprocal lattice. We present new, extensive small-angle scattering measurements, from which we are able to collect statistically relevant numbers of such peaks. This will allow us to infer more about their origin, The scattering results that are obtained on low concentration solutions show the existence of wavy layer structures, which may have a connection with a hexagonal structure at higher concentration. Most important is, however, that we found that the scattering spectra, time averaged in frames of 30 s or more, show a pronounced time dependence, be it over hours. The rate of change increases with decreasing temperature. Surveying the possible causes of such a dependence, we were led to the conclusion that, in the concentration range considered, the systems are not in equilibrium. In a narrow region of temperature, molar weight, and concentration, the system is still visibly in the process of phase separation. The underlying mechanism is considered.