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Replacement parts for MAYTAG MQU1556AEW FREEZER- VERTICAL | AppliancePartsPros.com

Sounds like it is a plugged drain tube (Item 10 in Section 2).

Check/clean the drain tube and the drain pan under the unit.
A turkey baster comes in handy here, often it just has to be flushed with warm water.
If it looks like gunk is growing in the drain tube flush it with a 10% bleach solution, wait 10 minutes and then do it again. This should kill and flush out the algae. Just be careful to not overflow the drip tray.

make sure that the freezer floor to the drain is clean as anything that impedes the water flow may allow it to freeze before it drains out.
A light waxing sometimes helps,

The heater just melts the ice off the evaporator coils and then it runs out the drain so I do not think it will have any effect on your icing problem.

Perhaps check your temperature, It should be between 0 and 5 degrees F.
Maybe it is too cold and the water is freezing before it can get to the drain.

Check/clean your door seals. Could be they are letting warm moist air into the unit and there is just too much frost on the evaporator coils. Sometimes the hinge side seal will grab onto the frame and not seal correctly. A light coating of white lithium grease or vaseline etc. usually fixes this.

There is a jiggery pokery fix for freezing drains. If the drain is behind the evaporator cover. There is no picture of the heater but I think it is a calrod type. If the heater is the glass type I would nor recommend the following.

Take a length of bare 14 or 12 gauge copper wire. Wrap it snugly around the heater a couple times and then route it down the drain tube an inch or two.
Then when the heater comes on the wire will also heat up some and also defrost the drain.

It is a good idea to force a defrost cycle after doing this just to be sure that the wire just gets warm and not hot as you do not want to start melting things.

Just want to add one more response. When I finally pulled the freezer out and loaded it on my truck there was the problem. The hose is routed in not the best of fashions and it was kinked. You could see where there was a crud build up before the kink even. I am totally in awe of you and your company that never once tried to sell me something that now is so very clear I did not need! I am impressed indeed. I would that everyone used your services. Mahalo