The possibility of neutron-mirror neutron transition has recently been discussed both from theoretical and experimental perspectives. We point out that such a transition would imply mass loss in neutron stars leading to a significant change of the orbital period of neutron star binary systems. Known limits on the period changes of such binaries therefore put strong limits on the above transition rate and hence on the n-n′ mixing parameter ϵ′. These considerations exclude a large range of ϵ′ even if the n-n′ mass difference is δm′ as large as a few MeV. Our limits also exclude a large range of the values required to explain the neutron decay anomaly via n-n′ mixing.