The first 2 photos show the underside of the shelf and the wire bracket that holds it in place, next 2 show it in place. When it was new it probably worked quite well, but as plastics age they become stiff and brittle. Just take off the 2 brackets that are there and install a new shelf on a hinge, make sure there is clearance for the bunk bed to swing up around the shelf. If there is not enough clearance you will have to come up with a removeable design for the shelf.
Check out the "70's flower power on the add a room!!