There are a few ways to track down this kind of info.
If the deactivated gameobject has an FSM that's receiving an event to deactivate itself you can right click on the event in the Debug Log to see who sent the event.
If it's just an FSM deactivating an object it's a little more difficult. It's probably the result of an Activate Game Object action, so I would right click that action in the Action Browser to see everywhere that action is used. Then start using the log or breakpoints to narrow it down further.
You could also pause the game right after the object is deactivated and examine the FSM logs for likely candidates.
NOTE: Preferences > Debugging > Forward Playmaker Log to Unity Log will dump all FSM logs to the Unity Console, sometimes making it easier to follow the program flow.
