Conditions for disk instability in low-mass X-ray binaries (LMXBs) have been recently considered with X-ray irradiation of the disk included. Conservative evolution was generally assumed, which, however, fails in wide LMXBs with a neutron star primary (NLMXBs). If the orbital period of an LMXB is long enough, the mass transfer rate becomes super-Eddington, and the evolution is likely to be nonconservative. Adopting the Eddington limited accretion hypothesis, we have calculated the evolution of NLMXBs driven by nuclear expansion of the secondary, and obtained a modified boundary between persistent and transient behavior in NLMXBs. We briefly discuss the applications to low-mass binary radio pulsars (LMBPs) and suggest a new scenario for the progenitor system of the bursting X-ray pulsar GRO J1744-28.