This paper explores the application of deep learning techniques to cryptanalysis, focusing on the Simplified Advanced Encryption Standard (S-AES). Unlike prior studies, which primarily analyzed small datasets and achieved limited success in key recovery, our work systematically evaluates the performance of various neural network architectures—including Convolutional Neural Networks (CNNs), Multi-Layer Perceptrons (MLPs), and Recurrent Neural Networks (RNNs)—on significantly larger datasets across Counter (CTR) and Electronic Codebook (ECB) modes. Our experiments demonstrate that RNNs outperform CNNs and MLPs in capturing cryptographic dependencies, achieving a training accuracy of up to 98.50% and a validation accuracy of 97.20% in key prediction tasks, surpassing previously reported results. Furthermore, while deep learning models traditionally struggle with generalization in cryptanalysis, our study presents key insights into mitigating these limitations, particularly in structured encryption settings. Despite the challenges posed by key space expansion and cryptographic obfuscation, our findings indicate that deep learning-based approaches, when properly configured, exhibit greater potential than previously suggested. This study advances the field by demonstrating the most successful deep learning-driven cryptanalysis of S-AES to date, providing a comparative benchmark, and outlining future research directions to further improve neural cryptanalysis.