Ok, now we know that the code-block got executed. Have you already tried to click the game window once? Sometimes, if Unity loses the focus, the user input does not work as expected.
For testing purposes, create a new script and a new scene. In Update, toggle the
Cursor.visible value via user input. A simple if-statement and its block should do the job. Then test the script in your scene. If that works, the issue must be somewhere in or near the HandleDeath method. If the toggling in the test scene does not either, there might be a general problem in Unity.
Which version of Unity do you use?