So, I'm very new to Starcraft II: Wings of Liberty, and I just purchased the game. I noticed that sometimes, Starcraft automatically saves, but sometimes, it doesn't. For example, when I finished a mission, it automatically saved that I finished it. On the other hand, when I purchased something from the armory and exited the game without pressing the "SAVE" button in the menu, it wouldn't save that I bought the item. When does Starcraft automatically save, and when do I manually have to press the "SAVE" button? Thanks.
Starcraft 2 automatically saves whenever you reach a checkpoint. This will only happen while playing missions. So when outside of missions, e.g. in the Armory, if you make changes, you will have to save before quitting if you want to preserve them.
As a general rule, checkpoints occur when you just reached an objective. I think that this only occurs for main objectives, not the bonus objectives. But I'm not entirely sure. The end of the mission always saves.
My suggestion would be that you save before quitting unless you want to revert to a previous save. The auto-saves are useful more for reverting than to maintain current progress. So if you complete two objectives but die before completing the third, you can revert back to when you completed the second objective with the auto-save. If you want to stop playing the game and resume from that point later, you should always save.
You may also want to save manually between objectives so that you can revert to that point. For example, you may want to save just prior to attempting an objective. That way you can try different tactics without having to repeat the building and development phase.