Is the unique asset deck reshuffled when cards are discarded?
The unique asset cards are still asset cards therefore they are discarded and not shuffled back in.

As Joey stated in a comment: 


  Considering the reason they (the assert cards) are shuffled right back
  in is likely to retain the variety of these "double-sided same on one
  side different on the other" cards, the unique assets are likely
  handled like assets and artefacts.


Also, the unique assets are unique. Which means that, from a story telling point of view, you cannot get the same one twice within a game. It would make no logical sense.