Spectral diffusion (SD) in PMMA doped with H 2 -TPP is investigated at 4.2 K on a time scale of 3 10 6 s via optical hole burning. Two contradictory (in frames of the TLS model) results are obtained. The first is the absence of aging effects which put the upper limit for the TLS relaxation times to tens of minutes. The second is an intensive superlogarithmic SD on the whole time scale of the experiment, which evidences the presence of very slow relaxations, independent of the sample history on the time scale of up to 2 months. The presented results provide the clear evidence of the deviation of SD behavior from the TLS model predictions at moderately low temperatures. The concept of structural relaxations is applied for a qualitative interpretation of the experimental data.