I think it was published in Fantasy and Science Fiction magazine sometime in the 1960s. The basic idea that I remember was that a guy kept getting phone calls on a daily basis asking whether he could see the sun. Finally, there was a cloudy day where he told the caller that he couldn’t see the sun, at which he heard the caller say in the background to someone else, something like “It’s OK, he can’t see it, you can take it away now.”
Ring any bells?
The Question by Laurence M. Janifer and Donald E. Westlake.
The early details don’t fit, and I’m pretty sure it’s not the same story–I remember the sun bit, but Heinlein’s “THEM” is the same principle with a similar ending.
It might be reprinted in Asimov’s various books of science fiction or fantasy short, short stories.
ETA: Damn you, Troutman < shakes fist > 
That’s it! Thanks! I remembered the story from reading it when I was 11 but had no idea where to find it again.
Heinlein’s “Them” ruined my life. I read it at a very impressionable age…and the “impression” is less like a divot and more like a sucking chest wound.
(When I was reading Heinlein’s “Job” and there was a passing reference to “The Glaroon,” I screamed out loud.)
Heinlein’s story is “They”.
He’s on to us!
Here’s a list of places that “The Question” has appeared Title: The Question - I’m guessing that you read it in “100 Great Science Fiction Short Short Stories”
Yep! And, if that ain’t enough, I literally did experience seeing it bucketing with rain out the front door…and clear and sunny out the back door!
(But there was a lovely rainbow, so it wasn’t all psychotic and paranoid. Just mostly.)
Nope. I had the original F&SF magazine. I was quite young when I read it, and it sort of blew my mind at 11 years old. That’s probably why the story has stuck in my memory for so long.
I did remember it incorrectly, however; I had thought there were a series of calls in the story on succeeding days, until there was finally a day when the sun wasn’t visible. Actually, the story recounted only a single phone call. But it was the punchline that stuck in my head all these years.
Yep - you even said so in the OP, and I read right past that part. Sorry.
Galactic Journey is an online fanzine that reviews science fiction 55 years late - yesterday they got up to this issue of the magazine [February 20, 1963] A merry chase (March 1963 Fantasy and Science Fiction) - Galactic Journey - I was delighted to find that another story that I’ve been idly trying to remember for ages was also in this issue “The Importance of being Important.”
And while we’re at it, since Andy L gave us the list of all appearances of “The Question”, I’ll give you the list of all the appearances of “They”: