The unstable plasma sheath resonance in a pulsed low-pressure hollow-cathode discharge was found to occur when the Bohm criterion fails. This happens during the transition of the discharge to a steady state. The duration of this transition is determined by the time required for the ion sound to cross the plasma volume. During this time a strong radio-frequency (RF) component may appear in the discharge current due to the instability of the plasma sheath near the cathode. The frequency of the RF oscillations is associated with the ion plasma frequency. The conditions required for the instability of the plasma sheath were investigated. We suggest a theoretical model which extends our earlier theory and explains the existing experimental results. The model also predicts a certain shift in the resonance frequency during the pulse, which was indeed discovered experimentally.