Abstract: :We consider the long-term tidal heating of stars by the supermassive black hole at the Galactic center, SgrA*. We show that the accumulated heat deposited by excitation of stellar modes over many pericenter passages can lead to a runaway disruption of a star at a pericenter distance that is 7-10 times farther than the standard tidal disruption radius. The accumulated heating may explain the lack of massive (~10 Msun) S-stars closer than several tens of AU from SgrA*.