We present new BeppoSAX observations of the TeV-emitting blazar Mrk 501 performed in 1999 June and a homogeneous reanalysis of all the BeppoSAX observations during the period from 1997 April to 1999 June. Recently published TeV spectra by the Cerenko Array at Themis, which are quasi-simultaneous with the 1997 BeppoSAX pointings, are used to constrain further the physical parameters of the jet in 1997 April with detailed models of the X-ray and TeV components. During the 1997-1999 period, the peak frequency of the synchrotron emission moved from about 100 keV in 1997 April to 0.5 keV in 1999 June. The shift in the peak frequency appears to be correlated with the long-term luminosity decrease. We interpret the results in the framework of a homogeneous synchrotron self-Compton model, discussing the evolution of the physical parameters of the emitting region under simple assumptions for the variability model. We also compute the expected variations of the TeV flux under the same assumptions.