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If the ice you are referring to is accumulating everywhere in the freezer not just at the drawers, like on the facing of the freezer when you open the drawer, then the issue is the unit is getting air in it from outside meaning something is not sealing properly letting outside air into the unit causing the moisture from the outside air to freeze eventually building up until it cause the problem you are having, what did the tech that came out do?
Ok since you have not responded yet , I will just say that it could be a door gasket issue allowing the air in or someone could have left the freezer door open etc; For a short term fix you can unplug the unit and let all the built up ice melt and that will fix it for a while but until someone figures out what is going on and where the leak is it will continue happening.
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