  Since neutrinos have mass differences, they could decay into one another. But
their lifetimes are likely long, even when shortened by new physics, so decay
likely impacts neutrinos only during long trips. This makes high-energy
astrophysical neutrinos, traveling for up to billions of light-years, sensitive
probes of decay. However, their sensitivity must be tempered by reality. We
derive from them thorough bounds on the neutrino lifetimes accounting for
critical astrophysical unknowns and the nuances of neutrino detection. Using
the diffuse neutrino flux, we disfavor lifetimes $\tau \lesssim 20$-450 s
$(m/{\rm eV})$, based on present IceCube data, and forecast factor-of-10
improvements by upcoming detectors. Using, for the first time, neutrinos from
the active galaxy NGC 1068, extant unknowns preclude placing lifetime bounds
today, but upcoming detectors could disfavor $\tau \sim 100$-5000 s $(m/{\rm
eV})$.
