Sepsis remains a major cause of mortality in intensive care units, largely due to delayed recognition and the limitations of current machine learning models that rely on retrospective, static electronic health record data. Although these models often show strong offline performance, their clinical translation is constrained by mismatches between training conditions and real-time bedside environments. Most existing systems depend on hourly aggregates or batch processing, introducing delays that reduce their usefulness within the narrow therapeutic window for intervention. In contrast, continuous vital sign streams generated by modern bedside monitors represent an underused source of real-time physiological information. This perspective argues that effective sepsis prediction requires a shift toward edge AI architectures that enable low-latency, privacy-preserving inference directly at the point of care. By treating physiological signals as continuous data streams rather than static records, and by deploying computation at the bedside instead of centralized cloud systems, models can better align with clinical realities. Such an approach could improve early detection, reduce alert fatigue through more context-aware predictions, and mitigate privacy, latency, and bandwidth challenges associated with cloud-based solutions. Ultimately, transitioning from retrospective modeling to real-time, edge-enabled decision support represents a necessary evolution in clinical AI, requiring close collaboration between clinicians, engineers, and data scientists to enable deployable, trustworthy, and timely sepsis prediction systems.