Thick frost on humid plate causes moisture problem

The cold plate that is attached to the back wall of the inside of my fridge keeps icing up. It affects the internal thermostat by telling it that it is plenty cold inside the fridge due to the ice/frost on the plate. When in reality it is not that cold, our jarred foods and bottled drinks end up "sweating" or forming condensation on the outside, and cold cuts last a mere three days instead of the normal week plus that they should, esp. when in the drawer.

Just yesterday I pulled all the food out of it and put it into a cooler, unplugged the fridge and went to work on removing the accumulated ice/frost which had built up to about 12 inches wide x 10 inches high (covering the height of the plate plus about 2 inches on either end) x about 3 inches deep! I removed all the ice without disrupting the Freon lines, cleaned the fridge out and wiped it down, and plugged the fridge back in. I then waited about ten minutes to put the food back in, and when I opened the door this morning, there was already a dusting of frost on the plate, surely accumulating as we speak.

I have the coldness set on 3 (out of 5+) and the energy saver feature set to "Reduce Exterior Moisture", as opposed to "Power Saver". What can I do to prevent the frost from building up and having to do this all over again in a few weeks?! Please let me know as soon as you can. Thanks in advance.