This was something straight out of a nightmare! A month that truly never ends The creep/horror factor is really amped up with the usage of children relaying the messages of time's increase via song. That'll make the hair on the back anyone's neck stand up!

I also think it was a smart choice to use different locations to show the passage of time. It's rather effective. And it also serves as a nice plot/setting device that reinforces the notion that trying to outrun or run away from time is fruitless. It can't be done.

The last thing I wanted to highlight was the ending. It was perfect! Your characters have worked really hard to avoid time and its agents of malice (i.e. court process servers) only to discover that the "cutest/silliest" thing that started the story off has come full circle to haunt them now.

I think the beginning gets a little muddled. I found myself having to reread it a few times because the dialogue is broken up by a long bit of character action before it's continued. I always recommend starting a scene with action rather than dialogue. When you start a scene with dialogue it can be jarring to the reader because we don't know our characters yet. You can get away with it longer fiction once you've established who the characters are. But in short stories and shorter pieces of fiction, it's almost always easier on the reader and more beneficial to start with action. By starting with action, it also eliminates the chasm between Philip's first line of dialogue and his second. I suggest something like:

Philip Armbester slid behind the wheel of his sedan. His wife, Sylvia, concentrated on her knitting as he grinned back at the office of the two-pump gas station. "I just saw the cutest little thing in there. A little kid, sitting on the cola dispenser, chanting some rhyme about the days in the months. Only, he's stuck on the first month and keeps repeating same line over and over."

It establishes your characters right away and shows a little bit about the dynamic between them. I think it's a more successful opening.

The last thing I wanted to comment on is that all of the discussion about Aunt Hetty sounds a bit forced to give information to the reader rather than service the characters or the progression of the plot. Philip pulls Sylvia aside and explains the situation to her as though she hasn't a clue as to what's going on. This conversation takes place and progresses the way it does to get certain information to the reader. Sylvia, who is also on the run from the process servers, should already have intimate knowledge of everything Philip has told her. It serves no other function and therefore sounds more like an info dump. There are more creative and reader-beneficial ways to sneak in this information through dialogue that isn't so straight to the point.

Example:

"Hey you're an astronaut. You've been to space at least six times before. And you're leaving for another mission tomorrow, right? I bet you're nervous, aren't you?"

VS

"Bill, six times in space and you're still bouncing your knee like it's your first go-around. Relax, man. Have a beer. After tomorrow you'll be a million miles away from cracking a cold one."