If it's inconsistent, yeah, probably not the "this is not my problem" problem.

A metal spoon in a disposable cup will get tossed in the trash pretty regular. (This is an issue for recyclers; neither paper nor plastics digesters like lumps of stainless steel...) I've seen the same thing happen with paper plates and metal cutlery, so I would think there's a possibility that this is what's going on. There's also the possibility (if it's the kind of health facility that feeds patients) that the patient kitchen has a sort of cutlery gravity and anything left in a patient room is
at risk of winding up there.