When me and a friend were building a map I was trying to run some tests with redstone and I tried to through a block onto a wooden pressure plate and the item appeared and then fell through my screen and vanished it did the same in a different location not on a pressure plate.
How to fix
Using NBT-Edit I compared my Level.dat file with a new fresh one.
In NBT-Edit the Byte "CanPickUpLoot" was 1, instead of the default 0. (In NBT-Edit: Data > Player > CanPickUpLoot)
For multiplayer use the player.dat files