Nowadays it’s rare for a postman to have to make a delivery face to face, but in the days when C.O.D. was common, he would usually have two bites at the apple. If he didn’t get an answer on the outbound leg of his route, he could — and probably was required to — try again on his way back. If you think about the possible ways to do a postal route, whether starting from a small-town post office or more likely from a car periodically parked, you would usually go up one side of a street and then back down the other side, whether immediately on a dead end or as part of a larger circuit. Either way, this gives you a second chance (by crossing the street) to make that special delivery.

The punchline to a joke (“Is that your lover?” “No, the postman always rings twice” sort of thing) doesn’t fit the plot of the novel; nor does a postman who rings the bell twice at his one attempt at delivery. But the postman making his second attempt at a delivery fits the story perfectly, and as an everyday postal procedure of the times it seems overwhelmingly likely.

2 possible answers:

On his morning delivery, out of respest for housewife working inside the home away from the doorbell (hanging laundry in the backyard, etc.), the Postman would ring twice.

The better explaination is that the Mail was delivered TWICE a day in the 1930′s and “40′s. It was common respect to ring the doorbell upon delivery. Hence, on their afternoon return roun, there would come the 2nd doorbell ringing. If you missed the morning delivery, the doorbell would ring again (TWICE) for afternoon delivery. At least, the 2 a-day delivery was prominent in the Midwest back then.

Mick

In the preface to Double Indemnity, Cain recounts how he showed the manuscript of The Postman Always Rings Twice to Vincent Lawrence, and continues:

Lawrence liked it, and even gave me a title for it. We were talking one day, about the time he had mailed a play, his first, to a producer. Then, he said, “I almost went nuts. I’d sit and watch for the postman, and then I’d think, ‘You got to cut this out,’ and then when I left the window I’d be listening for his ring. How I’d know it was the postman was that he’d always ring twice.”
He went on with more of the harrowing tale, but I cut in on him suddenly. I said: “Vincent, I think you’ve given me a title for that book.”
“What’s that?”
“The Postman Always Rings Twice.”
“Say, he rang twice for Chambers, didn’t he?”
“That’s the idea.”
“And on that second ring, Chambers had to answer, didn’t he? Couldn’t hide out in the backyard any more.”
“His number was up, I’d say.”
“I like it.”
“Then, that’s it.”