No, there's no spring on that "oddments tray" retrofit hinge (or the original one for that matter).
I spent the first two years fixing broken plastic bits on my boxster. Ugh.
Try adding some oil sometime to see if the flexible, accordion-style plastic oil filler tube has a crack in it. If you smell burning oil after adding oil, that's because it's cracked and leaking on your passenger side exhaust manifold
