I seem to have resolved the problem. The culprits are the defrost (bi-metal) thermostat and the defrost temp sensor. It seems that the problem is that because these components were faulty that the fridge enters defrost mode but never comes out of it. Once power is pulled, the system resets and begins the refrigeration cycle again. However, once the scheduled defrost cycle begins (in 4 hours for my model), it is stuck there and there is no more cooling.
I replaced both items for both fridge and freezer last night, and this morning was the first time that my fridge was still cooling after about 9 hours. I am hopeful that it will still be running when I get home from work today.
Just for documentation, I have a Samsung RB1855SL. The items that I used are Bi-Metal (DA47-10160H) and defrost temp sensor (DA32-00006W)
Replaced both for fridge & freezer compartments (4 items total). Both are fairly easy to get to once the evaporator covers are open. I would suggest anyone encountering this problem to give this solution a try as the components don't cost that much.
Edit: Just to add - the temperature sensors that allow for detection of actual temp in the fridge/freezer are actually fine. The system shows the set temps rather than actual temps when in the defrost cycle, even if the actual temps are significantly higher (this is confirmed in the service manual for my model).