  We investigate the dynamic stability of inspiraling neutron stars by
performing multiple-orbit numerical relativity simulations of the binary
neutron star inspiral process. By introducing eccentricities in the orbits of
the neutron stars, significant changes in orbital separation are obtained
within orbital timescales. We find that as the binary system evolves from
apastron to periastron (as the binary separation decreases), the central rest
mass density of each star decreases, thus stabilizing the stars against
individual prompt collapse. As the binary system evolves from periastron to
apastron, the central rest mass density increases; the neutron stars
re-compress as the binary separation increases.
