Don't know if this residential fridge was added post Mfg, but if so then it could be the type of valve used. Unless it was plumbed in with proper plastic fittings I suspect it may be a self-piercing clamp-on saddle valve. Self-tapping use a beveled syringe to pierce a horseshoe shape cut in the tubbing. On copper pipe this works because the cutout is bent into the copper tube, but on any form of plastic (PVC, Quest, Pex) the cutout with eventually return to it's original position, closing off the supply.
Keep this in mind on any home install. First sign is usually hollow ice cubes.