Data‐driven methods yield advantages in computational homogenization approaches due to the ability to capture complex material behaviour without the necessity to assume specific constitutive models. Neural network–based constitutive descriptions are one of the most widely used data‐driven approaches in the context of computational mechanics. The accuracy of this method strongly depends on the available data. Additionally, when considering inelastic materials, whose constitutive responses depend on the loading history, the accuracy and robustness of the approximation are influenced by the training algorithm. The applied recurrent neural networks exhibit reduced robustness in the presence of errors in the input. When capturing the history dependency using previously predicted material responses, occurrences of prediction errors accumulate over several time steps. An approach for achieving enhanced robustness of the predictions is based on extending the initial training dataset by iteratively generating adversarial examples, subjected to perturbations, based on the current prediction errors. In this contribution, a continuous self‐adversarial training approach yielding robust recurrent neural network constitutive descriptions for inelastic materials is presented. Compared to the iterative method it is based on, it exhibits significantly improved training efficiency. In order to demonstrate the capabilities of the proposed methods, numerical examples with datasets obtained by numerical material tests on representative volume elements are carried out. Validation of the results is performed using both test load cases from the numerical dataset, as well as application as a constitutive model in the finite element method.