  Neutrino mass sum rules are an important class of predictions in flavour
models relating the Majorana phases to the neutrino masses. This leads, for
instance, to enormous restrictions on the effective mass as probed in
experiments on neutrinoless double beta decay. While up to now these sum rules
have in practically all cases been taken to hold exactly, we will go here
beyond that. After a discussion of the types of corrections that could possibly
appear and elucidating on the theory behind neutrino mass sum rules, we
estimate and explicitly compute the impact of radiative corrections, as these
appear in general and thus hold for whole groups of models. We discuss all
neutrino mass sum rules currently present in the literature, which together
have realisations in more than 50 explicit neutrino flavour models. We find
that, while the effect of the renormalisation group running can be visible, the
qualitative features do not change. This finding strongly backs up the solidity
of the predictions derived in the literature, and it thus marks a very
important step in deriving testable and reliable predictions from neutrino
flavour models.
