The stopping cross sections (SCS) of Al2O3 and SiO2 for hydrogen ions have been measured by Rutherford backscattering relative to that of Al and Si, respectively, the velocity range being 3.45 < upsilon/upsilon(0) < 3.75 (equivalent to proton energies of 300 to 350 keV). Using these data we are able to re-evaluate the thickness of the targets used in our earlier measurements. Thus we get consistent stopping data in the velocity range 0.77 < upsilon/upsilon(0) < 5.4 (i.e., 15 to 730 keV for protons) for all targets and measuring methods used. The resulting absolute values are more accurate than our earlier data and consistent with those within the experimental uncertainties. Comparing our results for these compounds to stopping cross sections calculated for the corresponding mixtures we find that due to the influence of the chemical bond, the stopping in the compounds is less effective than in the mixtures; the largest deviations (up to 27% for Al2O3 and up to 14% for SiO2) appear at our lowest ion velocities. Furthermore we use our data to check whether the stopping behaviour of the oxides can be described by standard theoretical models, especially at low velocities where our experiment yields a stopping cross section proportional to velocity despite the rather large band gap of the insulators. We find that neither the density functional approach, nor linear response theory nor a binary encounter calculation can fit our experiment at low energies. Above proton energies of almost-equal-to 40 keV, the BEA calculation fits perfectly, while the LRT is in only qualitative agreement with our data. The reason for the failure of the theories at low velocities is still unknown.