Neutrino oscillation experiments and direct bounds on absolute masses constrain neutrino mass differences to fall into the microwave energy range, for most of the allowed parameter space. As a consequence of these recent phenomenological advances, older constraints on radiative neutrino decays based on diffuse background radiations and assuming strongly hierarchical masses in the eV range are now outdated. We thus derive new bounds on the radiative neutrino lifetime using the high precision cosmic microwave background spectral data collected by the Far Infrared Absolute Spectrophotometer instrument on board of Cosmic Background Explorer. The lower bound on the lifetime is between a few x 10^19 s and 5 x 10^20 s, depending on the neutrino mass ordering and on the absolute mass scale. However, due to phase space limitations, the upper bound in terms of the effective magnetic moment mediating the decay is not better than ~ 10^-8 Bohr magnetons. We also comment about possible improvements of these limits, by means of recent diffuse infrared photon background data. We compare these bounds with pre-existing limits coming from laboratory or astrophysical arguments. We emphasize the complementarity of our results with others available in the literature.