The fixed price BIN listings renew every month and that feature is called perpetual motion. The auto relist policy has been in place for two years now. Ok, I made up the PM name yet it fits. The BIN listings have to be manually closed by the seller if you want to end it. It goes in the 'unsold' barn after you end it manually.
Pretty sure the auctions don't auto relist even if they have a fixed price option so I believe your question relates to the fixed price BIN listings.
