Thats probably because the windowed mode is not borderless so if you are playing your max resolution with borders it hides the bottom part, since the bar at the top takes space. There is no fullscreen button generally on the task panel, it's full size windowed or small size windowed, or minimize, or close.
The hotkey to toggle full screen in most applications is alt+enter.
For me it works with window size:
1. Start game, press alt+enter to go windowed, close, start the game, its still in windowed.
2. Drag the game window smaller in windowed mode, restart the game, still keeps its size as you closed it.
3. Alt+enter to full screen, close the game, start, works.
Never went into the settings once here, it just "works"