I think you have an air leak.
Brian:There is no reason that Damp Rid would not work. I think that your real problem may be air leakage.I do not know what type of boat you are dealing with but check the lid. Our boat (H'31) did not have any insulation to keep air from getting in/out of the box. We went to Home Depot and got some window weather stripping. It is the small stuff (about 1/8"). You can just apply it around the edge of the lid. This should help with the frost and cut down on your power consumption too.