I accidentally fixed this yesterday by doing something which I now realise was similar to CarlosCanto suggestion:
"maximize" your window manually, that is, grab it by the corners and drag to fill up (almost) the screen, make sure you don't get to the actual maximum since the system will maximize the window for you, that should take care of the problem.
In addition to the original issue of the window going out of maximise mode on new file open I was getting another error message "Can't open the illustration. There is not enough room for the window; increase document area and try again". So what I did to fix this issue I manually resized the window by grabbing the corners and filling the screen. Then I think I clicked the maximise button and I say "think" as I was doing this without the intention of fixing the original problem, I just wanted to open my file, so I can't remember exactly. Then I opened a file and my window was maximised. Tried another file, and window stayed maximised. Shut down Illustrator and reopened and tested more files using double click on file in Windows Explorer to open or opening from Illustrator. Tested again today. Window is staying maximised and I was not getting any error messages..... victory is mine!!