Spectral diffusion (SD) in polymethylmethacrylate (PMMA) doped with free-base tetraphenylporphine is investigated at 0.5-4.2 K on a time scale of 3-10(6) s via optical hole burning. Two contradictory results-within the framework of the two level system (TLS) model-are obtained. The first one is the absence of aging effects at temperatures near 4 K which puts the upper limit for the TLS relaxation times at tens of minutes. The second one is an intensive superlogarithmic SD on the whole time scale of the experiment, which is evidence for the presence of very slow relaxations, independent of the sample history on a time scale of up to two months. The results presented provide clear evidence of a 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.