Managing copy sessions in a data storage system to control resource consumption

A technique for managing copy sessions in a data storage system supports active and inactive copy-session states and reclaims memory for inactive copy sessions to reduce their memory footprints. When a copy session transitions from the active state to the inactive state, the copy session persists certain copy-progress data in non-volatile storage and frees structures in memory previously storing that copy-progress data. The inactive copy session continues to run but performs no copying and consumes less memory. When the copy session later transitions back to the active state, the copy session reads the copy-progress data back into memory and resumes copying.