Sorry, what I meant was that it was worn so much only a small piece of it remains, i.e. the quality bar shows only a little piece (a "sliver". as in: Only a small sliver of the moon was visible, as it was new.).
Can your character make a new cap out of some hide (you can copy your save folder, try it to see if the results are different, delete the folder, and restore the original) and try with that cap, to rule out e.g. strange properties carried over from a cap made/bought in a fairly old version.