I had the exact same problem. What is happening is you are changing the focus from EQ back to your desktop. For whatever reason, EQ thinks you're in windowed mode even when you're in fullscreen mode. You can demonstrate for yourself what is happening by moving the window around before going full-screen and paying attention to what areas of the screen cause the game to minimize.
The only way I have found to correct this problem is to change the windowed resolution such that it is the same as the full screen resolution (whatever your monitor resolution is set to be).
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