Ice problem can’t be solved?

I recently had a repairman over to look at my fridge because the refrigerator was staying around 55 degrees. He checked the obvious...defrost heaters, thermostat, and timer and could find nothing wrong even though the ice build up on the bottom evaporator coil was so bad it was restricting air flow apparently. The timer is working, the heaters are heating, but the ice builds back up on the bottom coil within a few hours. I am leaning towards that being the problem. Does that sound feasible? He charged me for the service and told me it couldn’t be repaired.