The observation of neutron stars with masses greater than one solar mass places severe demands on any exotic neutron decay mode that could explain the discrepancy between beam and bottle measurements of the neutron lifetime. If the neutron can decay to a stable, feebly interacting dark fermion, the maximum possible mass of a neutron star is 0.7M_{⊙}, while all well-measured neutron star masses exceed one M_{⊙}. The existence of 2M_{⊙} neutron stars further indicates that any explanation beyond the standard model for the neutron lifetime puzzle requires dark matter to be part of a multiparticle dark sector with highly constrained interactions. Beyond the neutron lifetime puzzle, our results indicate that neutron stars provide unique and useful probes of GeV-scale dark sectors coupled to the standard model via baryon-number-violating interactions.