"Did this refrigerator come with the apartment? If it did, isn't the landlord responsible for it?"
Fridge is ours. Previous ancient unit died and not wanting to be slapped with an increase just went out and got our own.
As noted previously kitchen is small, and offerings > ten years ago for "apartment" sized fridges wasn't that great. Even today much of the 12 cubic foot or so units seem to come from Summit, Avanti and other off the wall brands, though WP does have one offering as well. None have the same nearly 12 cuFt space as the current GE. Especially liked the (comparatively) generous freezer space with full width shelf.
Do lots of baking/cooking and or stocking up on deals when on sale. Thus appreciate generous sized (for space it had to fit) unit. Other than the initial in warranty service call this GE fridge has proven remarkably reliable. Well for a General Electric modern appliance. Normally wouldn't touch anything "new" from that brand with a barge pole.
Have moved things about in both freezer and fridge to ensure vents aren't blocked, air flow paths clear.
Reached out to local appliance service person we use; and went through the sad tale of woe and misery. He knows us, and quickly went for a vein; asking what exactly in detail has one done. Explained about all the opening and closing of doors, removing of food to check evaporator fan motor, etc... His advice was to leave the fridge alone and get a hobby or something. If after a week or longer it still won't "shut down" call him back.
It was further explained pretty much what John L. already did; that this model series of GE fridges are designed to have things run a majority of the time. In very warm/humid weather that may go well into the 90% to 100% range. Local weather has been warm and very damp for weeks, and one constantly opening and closing fridge, messing with controls, taking things apart isn't allowing the appliance to operate properly.
Dressing down continued with remarking freezer and fridge temps are within normal range for "Cold" setting on control dial. If freezer isn't frosting over, fridge is keeping things cold but not freezing them then the appliance is working pretty much as it should. Ice forming at back of fridge along top of "fresh food" compartment was more result of ones continued opening of door allowing warm and humid air into the thing.
Mother Nature added further injury to this insult by sending a change of weather.
Wednesday was a nasty day of thunderstorms and wind as a cold front arrived. Result is by evening and over night not only had temps dropped, but so did dew point. So much so that even with just fans running it was rather chilly indoors.
At one point during night before going to bed was up doing some paperwork and noticed the place was quiet as a mausoleum. Went near kitchen and noticed fridge was "off", but not defrosting. First it had defrosted earlier (several hours ago), so shouldn't be doing so again. Also there are audible signals that come with the cycle (popping sounds caused by heat induced expansion, water gurgling, etc..), not a bit of it; the thing was totally off.
So it may seem John L, appliance person and everyone else was correct, the warm and humid temps may have been responsible for fridge working overtime to compensate.
At this point am going to leave things alone and move on. Will of course keep an eye on things, but from a distance. Last thing want to become is one of those bored know-it-all persons pestering appliance professionals with problems that don't exist, and won't take no for an answer.....