This paper proposes a method to introduce adversarial robustness to improve the performance of survival analysis (SA) models using neural networks (NNs). While neural networks are utilized to overcome the limitations of conventional generalized linear models, which often fail to capture complex data patterns, we propose an adversarial regularization-based loss function to address the performance degradation caused by data uncertainty. We utilize the CROWN-IBP technique to reduce the computational cost of the min-max optimization problem. Experimental results using 10 SurvSet datasets demonstrate that the proposed method (SAWAR) outperforms existing adversarial learning methods and state-of-the-art deep SA models in terms of NegLL, IBS, and CI metrics, achieving up to 150% performance improvement over baseline models. This demonstrates that the proposed method mitigates data uncertainty and improves generalization across diverse datasets.