I would either Wire Tie it in place or Screw it in place if you want to leave it in place. It will probably take itself down if you don't at some point?
On your Trailers older Brother
I have the shelf screwed together and it rides that way with the TV mounted to it too and I have had no problems with it like that.
I have to say I think the shelf is one of my favorite features of these and if you are a glasses wearer you will understand!