I know this works in XP and perhaps other versions. I had the problem that when minimized, the Serial Window disappeared completely but as one person said, when they MAXIMIZED the window, the monitor became visible.
The problem arose after changing video monitor settings, adding a new monitor, regardless of dual/single monitor configurations. It was the changing of the various resolutions that caused the issue. It was discovered that, in reality, the "minimized window" is simply out of the viewing area. Don't ask me how/why Windows get confused about the desktop sizing but it does. To get it back, verify that you do have a serial monitor active. Look down in the task bar and you should see the Arduino logo for each window that is being used. The serial monitor simply has "COM15" (for example). RIGHT-CLICK on this and you'll see the window options (MOVE, SIZE, MINIMIZE, MAXIMIZE, and CLOSE). Select MINIMIZE. When you do, and the problem exists, the MAXIMIZED window disappears and, poof!, no more serial monitor. It's simply out of the desktop viewing area. Now, RIGHT-CLICK the COM15 window (down in the task bar) again to bring up the MOVE, SIZE, etc menu as before. This time click ONCE on MOVE. You will see the cursor change to the 'directional' cursor. DON'T click or do but one thing: PRESS AND HOLD down the SHIFT key. This allows you to now use the ARROW keys to move the window. In my case, my Serial Window was about 10 feet off the left side (exaggeration), you get my meaning. Once I moved it back into view, happy days. I just about pulled all my hair out on this for a couple days. Good luck. (Sorry I don't have time to proof read this, or compress the language either. )