If a file has been saved and then a layer is renamed or the visibility of that layer is toggled it doesn't register as a change to the image so you cannot save the change.
1) Make any image
2) Save the image
3) Rename a layer and/or change it's visibility
4) File->Save has no effect
I assume that the Save function checks for changes in the undo history but these layer changes aren't recorded there.
*** This bug has been marked as a duplicate of bug 380437 ***