Sublimation has nothing to do with it – it has everything to do with the defrost cycle in a freezer.
As you noted, a freezer is essentially an enclosed box. Water vapor in the air freezes out, creating frost along the fridge sides and building up on the ice inside of the ice maker. Each time you open the freezer, water vapor from the outside air gets in, replenishing the water vapor inside of the freezer that had previously turned to frost.
To prevent the buildup of frost, freezers go through a periodic defrost cycle where they briefly allow the freezer to warm up to just above freezing. This melts the frost, which then drains through the freezer’s ventilation system and into an evaporator pan below the fridge. One consequence of this is that each defrost cycle causes a small amount of the ice to melt and then evaporate, shrinking ice cubes over time.
While sublimation is technically a thing, its so slow that you would never notice it on a human timescale and, again, ice builds up in a freezer due to the constant freezing out and reintroduction of water in the air.
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