The magnetic-field dependence of the frequency and damping time for the radial breathing mode of an optically trapped Fermi gas of 6Li atoms near a Feshbach resonance was investigated. For fields near 1080 G, a breakdown of hydrodynamic behavior was observed, which was manifested by a sharp increase in frequency and damping rate. It was observed that when the Feshbach molecular state in the singlet potential has a higher energy than the two-particle Fermi energy, the system becomes BCS-like. The results show that at higher fields near 925 G, the frequency decreased, and an abrupt frequency increased at a field of 1080 G, accompanied by rapid damping.