  Despite the fact that the solar neutrino flux is now well-understood in the
context of matter-affected neutrino mixing, we find that it is not yet possible
to set a strong and model-independent bound on solar neutrino decays. If
neutrinos decay into truly invisible particles, the Earth-Sun baseline defines
a lifetime limit of $\tau/m \agt 10^{-4}$ s/eV. However, there are many
possibilities which must be excluded before such a bound can be established.
There is an obvious degeneracy between the neutrino lifetime and the mixing
parameters. More generally, one must also allow the possibility of active
daughter neutrinos and/or antineutrinos, which may partially conceal the
characteristic features of decay. Many of the most exotic possibilities that
presently complicate the extraction of a decay bound will be removed if the
KamLAND reactor antineutrino experiment confirms the large-mixing angle
solution to the solar neutrino problem and measures the mixing parameters
precisely. Better experimental and theoretical constraints on the $^8$B
neutrino flux will also play a key role, as will tighter bounds on absolute
neutrino masses. Though the lifetime limit set by the solar flux is weak, it is
still the strongest direct limit on non-radiative neutrino decay. Even so,
there is no guarantee (by about eight orders of magnitude) that neutrinos from
astrophysical sources such as a Galactic supernova or distant Active Galactic
Nuclei will not decay.
