Consistent loss of tenth rocket piece

I've finished the quest for obtaining the rocket pieces, however, whenever I relaunch the game or go to another area in game (I.e. Old Gill's lighthouse, the Professor's Cave or my own house), the tenth piece mysteriously vanishes from the rocket and I have to go find it again.

This is on my second save slot so there's nothing tying it to social media.

A short FAQ on how to actually repair the rocket is needed as well.

Thanks!
~Kai