The influence of the quantum well potential on the carrier dynamics of holes bound to the acceptors in Be δ-doped AlAs/GaAs multiple quantum wells is investigated by far-infrared time-resolved spectroscopy using the Free-Electron Laser for Infrared experiments (FELIX). The lifetime of the 2p excited state of acceptors was measured as a function of the width of the quantum well and the temperature. It is found that the lifetime decreases monotonically with decreasing well width and is independent of temperature. We suggest that the relaxation process of the 2p → 1s is non-radiative and mediated via confined acoustic phonon modes, in particular, zone-folded acoustic phonon modes which arise from the periodic nature of the multiple quantum well samples. For one particular well width the lifetime was measured across the inhomogeneously broadened D-line as 30, 30, 70, and 105 ps for 43, 44, 46, and 47 μm wavelengths, respectively. We believe the latter is due to diffusion of the Be δ-doped atomic layer in the quantum wells.