Typically, some stories use circular structures for one of three purposes: 1) to show absolute futility, 2) to demonstrate some sort of unified, cohesive, but non-linear dream logic, or 3) a mixture of points 1 & 2.
Brian Keene's Fade To Null (in Unhappy Endings) employs point #3. It also taps into a tradition often seen in short fiction. It reads like a nightmare narrative, in that it displays a variety of surrealistic images -- for insance, a squirming eyeball-on-a-tentacle that makes noise without having an actual orifice. Yet, short stories that rely only on jarring imagery are usually not well crafted. Keene, after all, has a point. The center of the story has Alzheimer's patient and is elderly. The surreal imagery is a product of a brain that isn't functioning, and the circular nature of the story makes it horrific.
And the circular nature only works due to use of subtlety. Quiet often, it a narrator came out and said, "And every other day was the same thing," it would be heavy handed. The structure of the story is more of a cinematic loop, where the ending words are often cues that signal something very similar to the beginning.
Edit To Add: Holy shit, I was just cruising around amazon and saw Unhappy Endings listed for sale with a price tag $289.23. I still can't wrap my head and genre small press collectors.