  We reconstruct the neutrino mass as a function of redshift, z, from current
cosmological data using both standard binned priors and linear spline priors
with variable knots. Using cosmic microwave background temperature,
polarization and lensing data, in combination with distance measurements from
baryonic acoustic oscillations and supernovae, we find that the neutrino mass
is consistent with $\sum m_\nu(z)$ = const. We obtain a larger bound on the
neutrino mass at low redshifts coinciding with the onset of dark energy
domination, $\sum m_\nu(z = 0)$ < 1.46 eV (95% CL). This result can be
explained either by the well-known degeneracy between $\sum m_\nu$ and
$\Omega_\Lambda$ at low redshifts, or by models in which neutrino masses are
generated very late in the Universe. We finally convert our results into
cosmological limits for models with non-relativistic neutrino decay and find
$\sum m_\nu$ < 0.21 eV (95% CL), which would be out of reach for the KATRIN
experiment.
