We use the recent discovery of the first steady-state source of high-energy astrophysical neutrinos by IceCube, NGC 1068, to probe the lifetime of neutrinos. We look in the neutrino energy spectrum for characteristic features expected from the decay of neutrinos on their way to Earth. We find that present event rates, together with uncertainties in the predicted neutrino flux from NGC 1068, hinder our capacity to discern novel physics signatures in the data and place significant bounds on the neutrino lifetime. However, longer exposures and joint observations from upcoming neutrino telescopes and multi-messenger observations of NGC 1068 will improve the situation and reach significant sensitivities, enhancing our capability to probe neutrino decay, in particular, and novel physics signatures, in general.