Sequential recommendation models, models that learn from chronological user-item interactions, outperform traditional recommendation models in many settings. Despite the success of sequential recommendation models, their robustness has recently come into question. Two properties unique to the nature of sequential recommendation models may impair their robustness - the cascade effects induced during training and the model's tendency to rely too heavily on temporal information. To address these vulnerabilities, we propose Cascade-guided Adversarial training, a new adversarial training procedure that is specifically designed for sequential recommendation models. Our approach harnesses the intrinsic cascade effects present in sequential modeling to produce strategic adversarial perturbations to item embeddings during training. Experiments on training state-of-the-art sequential models on four public datasets from different domains show that our training approach produces superior model ranking accuracy and superior model robustness to real item replacement perturbations when compared to both standard model training and generic adversarial training.