In the nonlinear regime, the stability of resonantly driven systems, such as energetic particle driven modes in magnetically confined plasmas, is shown to depend on the presence and nature of an underlying damping mechanism. When resonant damping is involved, subcritical states can occur. In particular, purely nonlinear steady-state regimes can be postulated, whose destabilization threshold and saturation levels are calculated and validated using a reduced one-dimensional paradigmatic bump-on-tail model. The applicability of the developed model to realistic tokamak acoustic modes is assessed. It is shown that purely nonlinear steady-state regimes are possible under standard tokamak conditions.