We analyzed polarization characteristics of gammadion-shaped planar chiral nano-gratings (PCNGs), using Jones matrix and FDTD simulation. Optical activity (OA) was found to take place at wavelengths where long-lifetime modes appeared in the chiral layer. Among two kinds of resonance phenomena that concern the extension of the lifetime, guided-mode resonance and Fabry-Perot resonance, the latter was found to be a key to generate practically-important, broad peaks in the OA spectrum. Through the calculation of dispersion relations of Bloch modes in the chiral layer, we showed that the interference of multiple modes with group velocity dispersion played a critical role in the generation of such long-lifetime modes.