I have MS Office XP (which is "2002" for those who need the number) running on WinXP Pro.
I just copied some formatted text from a Word document, and pasted elsewhere (only to insure I really had copied what I wanted).
I then shut down Word, and pasted that text into another application, Outlook (which is also an Office application). The formatted text was pasted as expected.
I then shut down Outlook, so now I had no other Office application running. I then pasted into another application, Notepad, and the paste worked there as well (minus the formatting, naturally).
I then again opened Word and pasted there. The words I had, still in the Copy buffer, were still able to be pasted, and they were formatted.
So, what you described, is not how it works here. Sorry.
I suspect there may be a setting on your Word, or Office Suite, that says "clear out the buffer when I shut off the Office applications."
I do not know if such a switch exists. All I know is that the copy buffer maintains for me, even after all Office applications are shut down.