Airborne wind energy (AWE) systems are tethered flying devices that harvest wind resources at higher altitudes which are not accessible to conventional wind turbines. In order to become a viable alternative to other renewable energy technologies, AWE systems are required to fly reliably and autonomously for long periods of time while being exposed to atmospheric turbulence and wind gusts. In this context, the present paper proposes a three-step methodology to improve the resilience of an existing baseline control system towards these environmental disturbances. In the first step, upset conditions are systematically generated that lead to a failure of the control system using the subset simulation method. In the second step, the generated conditions are used to synthesize a surrogate model that can be used to predict upsets beforehand. In the final step an avoidance maneuver is designed which keeps the AWE system operational while minimizing the impact of the maneuver on the average pumping cycle power. The feasibility of the methodology is demonstrated on the example of tether rupture during pumping cycle operation. As an additional contribution a novel transition strategy from retraction to traction phase is presented that can reduce the probability of tether rupture significantly.