We report on a single crystal neutron spin-echo investigation of the low-energy dynamic response in the heavy-fermion superconductor UPd2Al3 in the vicinity of the antiferromagnetic wave vector Q(0)=(0 0 0.5). Well inside the superconducting phase, antiferromagnetic quasielastic scattering, which is present in the normal state, is absent for relaxation times up to 10 ns, equivalent to an energy resolution of approximately 1 microeV. This places strong constraints on possible models for this magnetic superconductor.