Browser fingerprinting has emerged as a significant technique for device identification, fraud detection, user authentication, and cybersecurity monitoring. Recent advances in deep learning have enhanced the capability of browser fingerprinting systems to identify users with high accuracy by extracting complex patterns from browser and device attributes. However, increasing model complexity has also introduced vulnerabilities related to adversarial manipulation, privacy risks, model generalization, and robustness under dynamic environments. This study investigates the vulnerability and robustness of deep learning-powered browser fingerprinting techniques within cybersecurity applications. Drawing insights from contemporary deep learning literature and recent developments in adversarial robustness research, the paper proposes a conceptual framework for evaluating security resilience in browser fingerprinting systems. The study synthesizes existing knowledge on deep learning architectures, federated learning optimization, physics-informed modeling principles, and intelligent edge computing to analyze robustness challenges. Findings indicate that while deep learning significantly improves identification performance, susceptibility to adversarial perturbations, fingerprint obfuscation, data drift, and privacy attacks remains a major concern. The paper highlights the importance of adversarial training, federated learning frameworks, explainable artificial intelligence mechanisms, and adaptive security architectures in strengthening future browser fingerprinting systems.