Unlike modern games with auto-save features, Metroid II requires you to actively save your progress. This is done at specific Save Stations scattered throughout SR388. These stations are easily identifiable by their distinctive glowing appearance.
To save, simply walk Samus into the Save Station. The screen will flash, indicating that your game has been successfully saved. It's highly recommended to save frequently, especially after acquiring new power-ups or defeating a Metroid. Dying without saving will send you back to your last save point, potentially losing significant progress. Always prioritize finding and utilizing these crucial save points.