We have investigated experimentally and by computer simulations the energy-loss distributions of low-energy ( keV) protons and deuterons transmitted through polycrystalline palladium thin films. In contrast to previous experiments on various transition metals we find that the stopping power of Pd is proportional to the ion velocity. Data of protons and deuterons are coincident within the experimental uncertainties, showing the absence of an isotopic effect on the stopping power of Pd in this energy range. The experimental results were analyzed and compared with Monte Carlo computer simulations and previous theoretical models. The difference in the velocity dependence of the energy loss of hydrogen ions in Pd with respect to other transition metals (Cu, Ag, and Au) is explained by a theoretical analysis based on the properties of the -electron bands of those elements.