I don't think maximum plates held was my problem—there were some plates right next to where I could move that I never managed to pick up even when I was standing still and had zero plates.
Having a maximum number of plates on the ground, plates that don't despawn, and a mechanic which changes where the player can stand (making some plates inaccessible) was not a good combination of mechanics. If you get knocked back while there's a plate on the ground, you'll never be able to pick that plate up. (And obviously the plates that I guess landed just a bit too close or far for you to collect make that worse, but that part presumably isn't intentional.)