Is the game running in "true" fullscreen, or a screen sized borderless window?
If you move the cursor out of the game manually and click the left mouse button, does the game lose focus?
I don't have Elite to test with, but Googling around, it seems the game has had many issues with mouse cursors vanishing, getting stuck, and not getting locked to the window.
What is the "Hardware Mouse Cursor" option in the ingame settings set to?