The cheese moves around the stage and you need to grate it when it's above the plate.
If the cheese isn't moving... that's the bug that has been baffling me for the entire duration of development. I have no idea why, but sometimes that level just breaks – I've never been able to replicate it consistently, but it's extremely rare, it only happened to me twice in two weeks. Restarting the game is the only way, sorry about it.