Predicting and avoiding critical load events is crucial for the reliable autonomous operation of airborne wind energy (AWE) systems. Such events can lead to actuator saturation, loss of steering authority, and increased structural stresses, eventually resulting in long-term degradation of the kite, tether, and ground-station components. The present study explores a data-driven approach to predicting tether force peaks, defined as instances in which the force exceeds a threshold set by the winch controller. The method is developed using a large-scale SCADA dataset from Kitepower's leading-edge inflatable V9 kite, including more than 1000 pumping cycles spanning 26 h of kite operation and covering a wide range of wind and operating conditions. Tether force peaks are detected and used to extract pre-peak time windows that capture the system behavior before each threshold exceedance. From these windows, statistical, temporal, and spectral features are computed from multiple kite, tether, and ground-station measurements. A supervised classification model is trained to distinguish normal operation from pre-peak dynamics. The proposed approach predicts critical load events 1 s in advance and shows strong generalization capability on flight data that was not used for training the model, correctly identifying 85.4 % of the critical load events (recall) and achieving a 90.9 % F1-score, a metric that indicates a strong balance between correctly detected events and false alarms. Moreover, the extracted features provide valuable insight into the system dynamics preceding these events. The obtained results enable preventive control actions, thereby improving the reliability of AWE systems.