We study the robustness of self-sustained oscillatory activity in a globally coupled ensemble of excitable and oscillatory units. The critical balance to achieve collective self-sustained oscillations is analytically established. We also report a universal scaling function for the ensemble s mean frequency. Our results extend the framework of the aging transition [Phys. Rev. Lett. 93, 104101 (2004)] including a broad class of dynamical systems potentially relevant in biology.