Why is the ice in my icetray disappearing?

You have a self defrosting refrigerator which is circulating cold dry air inside the box. The ice is subliming directly from solid ice to vapor and being carried off. If you want to stop it, put a sheet of aluminum foil the width of the tray across the top. But a "month or two" is too long to be keeping ice, it picks up flavors and loses air and tastes bad.

Mike's right: "sublimation" is the water in your ice transitioning from solid state to vapor state without going to liquid state in between. But it will happen in any freezer; it doesn't have to be self-defrost.

I learned this as a kid, when I tried to save some snowballs for summer play... :-)

Sublimation causes the cubes to become smaller. Sublimation is also the cause of "freezer burn". Any meat in the freezer is also losing water unless it is sealed airtight.