An illustrative data storage management system comprises “awareness logic” that executes on computing devices hosting storage management components such as storage manager, data agent, media agent, and/or other storage management applications. The illustrative awareness logic operates within each of these illustrative components, e.g., as a thread within processes of the storage management component, such as storage management core process, file identifier process, log monitoring process, etc. The awareness logic monitors the targeted process over time and triggers remedial action when criteria are met. Certain vital statistics of each process are collected periodically and analyzed by the illustrative awareness logic, such as CPU usage, memory usage, and handle counts. Criteria for corrective action include rising trends based on local minima data points for one or more vital statistics of the process. Other criteria include exceeding a threshold based on a logarithm function of the collected data points.