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Electricity network operators use computationally demanding mathematical models to optimize AC power flow (AC-OPF). Recent work applies neural networks (NN) rather than optimization methods to estimate locally optimal solutions. However, NN training data is costly and current models cannot guarantee optimal or feasible solutions. This study proposes a robust NN training approach, which starts with a small amount of seed training data and uses iterative feedback to generate additional data in regions where the model makes poor predictions. The method is applied to non-linear univariate and multivariate test functions, and an IEEE 6-bus AC-OPF system. Results suggest robust training can achieve NN prediction performance similar to, or better than, regular NN training, while using significantly less data.