Many physical systems exhibit marginally unstable periodic orbits, which are nonhyperbolic families of periodic orbits appearing as segmented line structures with zero Lebesgue measure coexisting with hyperbolic components in phase space. Orbits in their vicinity escape in a subexponential manner which is in strong contrast to orbits near unstable periodic orbits which escape in an exponential way. By selectively exciting a series of modes in a rounded D-shape microdisk containing an InGaAsP multiquantum well, we experimentally demonstrate that marginally unstable periodic orbits can support a much more robust lasing than conventional unstable periodic orbits. Through numerical computations, we also compare quality factors of modes localized on marginally unstable periodic orbits and on stable periodic orbits.