The title post makes this a pretty mysterious issue to deal with, you might get more replies if the title described the issue in some way.
I don’t know what’s happening in the scenario you’re describing but I have found that issues with avid windows that in some way obscure themselves and can’t be moved simply by dragging the window around as you normally would, it can help to try removing additional monitors from the system thus hopefully forcing a new window placement on your single monitor which you can then save by quitting avid. Then you can plug your additional monitors back in and start Avid again and hopefully the window placement has been saved to your user account from the previous session and will be visible on your main monitor ready for you to move them where you’d like them. This solution is mainly for dealing with windows that have decided to position themselves outside the borders of the visible screen space on a monitor rather than windows that have decided to disappear altogether, but it might work for this too.
It also sounds like, if they appear on quitting, the windows are somehow appearing behind other windows and are there all along, perhaps it would help to use the cmd+~ key combination and see if that returns the window to the top of the screen.
Failing that, if you haven’t tried it, messed up interfaces are also often fixed by creating a new user with everything stock standard. If that fixes it, you know it’s an issue with your user settings and you can figure out what to do from there.