Why did Diamond brand propane fridge have droplets of water build up turn to ice build up fast after defrosting?

SOURCE: the freezer has ice build up on vents

Cooling is poor For an overall understanding of how refrigerators should work, read about refrigerators in the How Things Work section of our website. A refrigerator or freezer that is cooling, but cooling poorly, may have a problem in one of several areas:

Evaporator coils
Condenser
Poor cooling is often the result of a heavy frost build-up on the evaporator coils or a condenser that is clogged with dust, lint, and dirt. 

Evaporator coils Poor cooling is often the result of a heavy frost build-up on the evaporator coils. You can't see these coils without removing a panel on the inside of your freezer. A sure sign that there is a build-up is the presence of any frost or ice build-up on the inside walls, floor, or ceiling of the freezer. Such a frost build-up usually indicates a problem in the self-defrosting system or damaged door gaskets.

The refrigerator is supposed to self-defrost approximately four times in every 24 hour period. If one of the components in the self-defrosting system fails, the refrigerator continues to try to cool. Eventually, though, so much frost builds up on the evaporator coils that the circulating fan can't draw air over the coils. There may still be a small amount of cooling because the coils are icy, but with no air flow over the coils, cooling in the refrigerator compartment is quite limited.

Here's an inexpensive, though inconvenient, way to determine if the problem is with the self-defrosting system. Remove all of the perishable food from the refrigerator and freezer, turn the thermostat in the refrigerator to Off, and leave the doors open for 24 to 48 hours. (Be sure to have several towels ready in case the melting frost and ice causes the drip pan to overflow). This allows the refrigerator to defrost "manually." When the frost and ice build-up has completely melted away, turn the thermostat back to a normal setting. If the refrigerator then cools properly, it indicates a problem with one of three components in the self-defrosting system:

• The defrost timer



• The defrost thermostat (also called the bi-metal switch)



• The defrost heater

If it still does not cool properly, there may be a problem with the refrigerant level or the compressor. You may need to consult with a qualified appliance repair technician to further diagnose the problem 

Condenser Self-defrosting refrigerators all have a set of coils and a cooling fan, usually under the refrigerator, that need to be cleaned regularly. If these coils get coated with dust, dirt or lint, the refrigerator may not cool properly. The coils may appear to be a thin, black, wide radiator-like device behind the lower kick-panel. To clean them, disconnect the refrigerator from the power source, use a refrigerator condenser brush (see the Appliance Accessories section) and your vacuum cleaner to clean the coils of any lint, pet hair, etc. You may not be able to get to all of the condenser from the front, it may be necessary to clean the remainder of the condenser from the rear of the refrigerator. 
also click the links below for more help
It's stopped completely 
It's not cool
Cooling is poor
It's noisy 
It leaks
The freezer compartment is icing up
The food in the refrigerator freezes
There's water dripping inside the refrigerator
The refrigerator never cycles off
The ice maker has a problem
There's an ice- or water-dispensing problem

SOURCE: Fridge Freezer ices up

easy....drain hole iced up....when it defrosts it will flood base of freezer....24 hour switched of to defrst it will cure it

SOURCE: automatic defrost no longer works

If freezer is icing up, you might have a defrost problem. Frost free models have a heating element that is controlled by a timer to automatically defrost ice, defrost timer turns on defrost heating element every 12 hours to melt ice in freezer and allow good air flow.
You can test defrost element with an ohm meter(located inside freezer coils-will have two wires going to a plug connection), if OK replace defrost timer (located in various places depending on make and model

SOURCE: Ice build-up in lower freezer. We replaces the

If the evaporator coils behind the back panel of the freezer are icing up because of auto defrost failure that will stop the circulation of cold air and eventually affect the freezer too.
How to check everything
http://www.acmehowto.com/howto/appliance/refrigerator/refrigerator.php

check , defrost heater, defrost thermostat. If the heater and thermostat are ok it’ll be the adaptive defrost control. Part 13 in this diagram.
http://www.searspartsdirect.com/partsdirect/getSubComp.pd?modelNumber=MSD2756GEW&productCategoryId=0165000&brandId=3048&modelName=SIDE-BY-SIDE-REFRIGERATOR&diagramPageId=00002&componentDescription=CONTROLS&documentId=M0404275&backToLink=Return%20to%20Sub%20Components%20list

SOURCE: DANBY dbc657bls This is a beverage fridge by

you have a door seal leak, the ice is from outside air getting into the cooler, you might also check for an air leak it the service door in the bottom back of the cooler.