Adversarial training enhances the robustness of Machine Learning (ML) models against adversarial attacks. However, obtaining labeled training and adversarial training data in network/cybersecurity domains is challenging and costly. Therefore, this letter introduces Adaptive Continuous Adversarial Training (ACAT), a method that integrates adversarial training samples into the model during continuous learning sessions using real-world detected adversarial data. Experimental results with a SPAM detection dataset demonstrate that ACAT reduces the time required for adversarial sample detection compared to traditional processes. Moreover, the accuracy of the under-attack ML-based SPAM filter increased from 69% to over 88% after just three retraining sessions.