Hi
I am getting exactly the same problem with some text files placed by someone else as I never link text files.
I have tried turning it off and on again with no luck, I can embed graphics but the unlink option is also missing for me in menu customisation.
I am not sure if this is the answer but the files which cannot be unlinked are missing for our subversion directory but if I place a new text file with linking on the unlink option appears and works so it may be that if InDesign thinks the files are missing it cannot unlink?