The magnetic moment relaxation in polycrystalline YBa2Cu3Ox material has been studied using zero-field-cooled measurements. The temperature dependence of the relaxation rate shows a field-dependent maximum. When the oxygen content is reduced, the maximum shifts towards lower temperatures. This shift is directly related to a decrease of the intragrain critical current density in the oxygen-deficient material, inducing a decrease of the field H* for complete flux penetration. The characteristic activation energies for depinning in the oxygen-deficient material are below 20 meV.