The disclosed embodiments relate to a system that automatically adapts a prognostic-surveillance system to account for aging phenomena in a monitored system. During operation, the prognostic-surveillance system is operated in a surveillance mode, wherein a trained inferential model is used to analyze time-series signals from the monitored system to detect incipient anomalies. During the surveillance mode, the system periodically calculates a reward/cost metric associated with updating the trained inferential model. When the reward/cost metric exceeds a threshold, the system swaps the trained inferential model with an updated inferential model, which is trained to account for aging phenomena in the monitored system.