We report on a new analysis of instabilities in close neutron star binaries based upon (3+1) dimensional general relativistic numerical hydrodynamics calculations. When a realistic equation of state is employed, orbit calculations for two 1.45 M⊙ neutron stars reveal surprising evidence that general relativistic effects may cause otherwise stable stars to individually collapse prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than post-Newtonian estimates. Thus, there is possibly a violent change in the system which endures for a number of seconds, yet which should also reflect a characteristic millisecond substructure due to the orbit period. Implications of this new result for cosmological gamma-ray burst models are discussed.