While machine learning has significantly advanced ad and tracker detection, existing systems face critical challenges in practice. They are vulnerable to adversarial attacks (57-92% evasion rates), fail to generalize to unseen domains due to data contamination, and suffer performance degradation over time, requiring costly retraining. To address these challenges, we present AdVersa, a client-side framework for robust and practical ad and tracker blocking. AdVersa leverages novel, hard-to-perturb latent features from code and URL embeddings to deliver state-of-the-art performance. On a 2.74M-request dataset, our results show that AdVersa achieves a 98.23% F1 score, twice the robustness against adversarial attacks, and strong generalization to unseen domains (91.47% F1 score). For sustainable protection, we demonstrate that a low-cost pseudo-labeling strategy can maintain near-optimal accuracy, reducing maintenance overhead by over 99.8% compared to filter-list curation. Finally, we implement AdVersa as a lightweight, standalone client-side application that ensures user privacy by operating without external dependencies.