I've noticed that if I have the TP9 main window maximized when I close the application, when I re-open it, TP9 opens with the window filling the entire screen but not actually maximized - the little icon next to the red "X" at the right end of the title bar is indicating that the window is not maximized, the very top of the window title bar is slightly off the screen, and I can see part of the left and bottom window borders and actually grab and drag them - window borders do not exist for a maximized window. When I click on the title bar icon to maximize the window, it maximizes as expected.
I had a look in startup preferences, and "Remember window size and position" is checked.