Unfortunately, it’s more than just ‘maintenance’.
I had a Frigidaire Stainless/frostless side-by-side model with icemaker, predating the newer high-efficiency models (which run all the time, by the way, but apparently use less power). One day I noticed it wasn’t cooling the fridge part either. I also decided to do some ‘maintenance’ and noticed some stains on the floor & in the pan that looked like it could be oil from the system. Called a repair person, he gave me a line (I’m a technician/geek), said he’d have to take it back to his shop for diagnosis and gave me a quote for replacing the compressor. I told him I’d give him a call if I decided to fix rather than replace (intending on calling around). $80 diagnosis bill.
Called around to acquaintances, got a referral to a former LEO running his own thing on appliance repair, stopped by & spoke to him, got some ‘free advice’ and the fridge has been working ever since.
The free advice?
Apparently the ‘frost-free’ models can freeze inside the panels. Hairdryer won’t work. He said “let it set unplugged & open for 2-3 days and then plug it back in & try it out”; it had already sat for 4 days in the garage because I’d already replaced it with a high-efficiency Frigidaire Gallery side-by-side with icemaker (which I highly recommend after owning for 3 years). I let the fridge set for only 2 days, but that was apparently not enough.
Basically the same fix/result you had, but with no ice symptoms (but spots on the floor, which was the reason I called a tech) and also involved an unscrupulous technician. The spots, I surmised, were from copper oxide & condensation; the fridge still works to this day in my former employer’s breakroom.
My conclusion was that the guy was going to call me from his shop, tell me it ‘was the compressor’ and sell it used after defrosting it himself when I told him I was replacing it. Crooked a$$hole.
When the fridge gets a little cold on the inside bottom, or along the inner sides, but is not getting cold enough, if it's not low on coolant, and the compressor and fan work, etc, --- it can be the door switch.
Moisture can seep in. ruining that switch -- which typically 'works' by cutting power to the fan and sending power to the light circuit when the door is open.
When it doesn't work, when the door is in closed position, instead of the switch then being depressed and making connection in the fan circuit--- it doesn't, which is why in this instance a refrigerator can be getting a little cold at (inner) bottom or sides, but not cold enough overall, since the air isn't circulating, making the 'fridge sense it's cold enough, shutting down the compressor, etc.
The door switch often as not, if needing replacement, can be pried out of the recess they are set in, having only a few wires that will need be re-connected to a replacement switch.
Switches can be had (if going through an industrial supply house, rather than Sears, or a place which sells and services appliances ) from around $5 to $15.