I've never seen that before. Not sure what it is, but I have a similar thing in some other software. In my case, a new software package updated some of my fonts and changed the file names or locations slightly in such a way that older documents thought the specified font was missing. Word will automatically substitute in these cases. If something happened that could have renamed your font, reinstalling the old font file may help.

Another theory is that the font is not really specified as Times New Roman in this document. If the font was specified as "Body" then the font will automatically convert to whatever is set as the body font (like with website design). If you change the font back to Times New Roman and then save the file, will it open as Times New Roman the next time?