I just confirmed something I suspected. I already knew that if you're killed after getting an enemy trophy, and choose to give up, you retain that trophy.
So I tested the following: I got the Rayquaza trophy, then on the next screen I exited back to the map via the menu. I didn't get the "you got those trophies" screen like when you die and not continue, or finish the level, so I thought the Rayquaza trophy was lost (no big deal, it's quite easy to get in Intense). But I went to the trophy collection, and sure enough, there it was. So, all of you worried about losing a trophy after getting it, just quit back to the map.
I also noticed that during the boss battle, no more than one item spawned at a time. It may be a good idea to throw these unwanted items offscreen as soon as you can while you wait for the stand to drop.