A method for investigating the degree of stability of nonlinear limit cycle oscillations (LCO) observed in an aeroelastic system is presented. The system considered is a typical section airfoil model with a free-play nonlinearity in the control surface stiffness. Stability information of the LCO is obtained by fitting a map to an ensemble of perturbation induced transient data and then observing the properties of the map as a function of flow speed. Stability analysis of the linear subdomains only can suggest approximate locations of global system features such as LCO onset and flutter. Whereas the proposed method allows for the nonlinearity and thus can indicate impending stability transitions with much greater accuracy.