“Always be closing” (the ABC’s of selling) dates in print to at least 1950. The phrase was popularized by David Mamet’s awarding-winning play, Glengarry Glen Ross, which opened on Broadway in 1984—and the critically acclaimed 1992 film of the same name. Mamet’s drama involved shady real estate sales, but “always be closing” has also been used in the sales of financial products.
   
 
Wikipedia: Glengarry Glen Ross
Glengarry Glen Ross is a 1982 play written by David Mamet. The play shows parts of two days in the lives of four desperate Chicago real estate agents who are prepared to engage in any number of unethical, illegal acts—from lies and flattery to bribery, threats, intimidation, and burglary—to sell undesirable real estate to unwilling prospective buyers. The play draws partly on Mamet’s experiences of life in a Chicago real estate office, where he worked briefly in the late 1960s. The title of the play comes from the names of two of the real estate developments being peddled by the salesmen characters, Glengarry Highlands and Glen Ross Farms.
 
Mamet had sent the play to Harold Pinter for comment, who admired it and, as an associate director to Peter Hall, recommended it for production. As a result the world premiere was at the National Theatre in London on September 21, 1983, where Bill Bryden’s production in the Cottesloe was acclaimed as a triumph of ensemble acting.
 
The play opened on Broadway on March 25, 1984 and closed on February 17, 1985. The production was directed by Gregory Mosher and starred Joe Mantegna, Mike Nussbaum, Robert Prosky, Lane Smith, James Tolkan, Jack Wallace, and J.T. Walsh. The production was nominated for four Tony awards including Best Play, Best Director, and two Best Actor nominations for Robert Prosky and Joe Mantegna, who won the production’s one Tony.
     
Google Books
Successful Investment Salesmanship:
A series of lectures given in a course on investment salesmanship sponsored by the Boston Investment Club and Boston University
By Boston Investment Club
Published by Barron’s Pub. Co.
1950
Pg. 46:
You know that the ABC’s of selling are, “Always Be Closing.”
Pg. 47:
Well, always be closing, the ABC’s of selling, close, close, close as you go along.
   
Google Books
Textbook of Salesmanship
By Frederic Arthur Russell, Frank Herman Beach
Edition: 6
New York, NY: McGraw-Hill
1959
Pg. 435:
... closing a sale is as simple as ABC— Always Be Closing. it isn’t quite that simple, but the idea is sound.
     
Google Books
Marketing Communication:
Modern promotional strategy
By Frederick E. Webster
New York, NY: Ronald Press Co.
1971
Pg. 308:
A salesman may learn a “rule” of selling (for example “ABC,” “Always Be Closing”) long before he learns how to apply that rule.
     
Google Books
Pastoral Assertiveness:
A new model for pastoral care
By Paul A. Mickey, Gary Gamble, Paula Gilbert
Published by Abingdon
1978
Pg. 89:
The student forgot the ABC’s of selling — always be closing!
 
Google Books
Glengarry Glen Ross
By David Mamet
Edition: reissue
New York, NY: Grove Press
1984
Pg. 13:
ALWAYS BE CLOSING.
Practical Sales Maxim
 
Google Books
David Mamet
By C. W. E. Bigsby
Published by Methuen
1985
Pg. 114:
...a practical sales maxim- ‘Always Be Closing’. The essence of salesmanship, in other words, is to imply both that the customer is getting a bargain and that he or she is in a position to take advantage of the seller.
   
Internet Movie Database
Memorable quotes for
Glengarry Glen Ross (1992)
Blake: A-B-C. A-Always, B-Be, C-Closing. Always be closing, always be closing.
     
YouTube
Alec Baldwin - Best performance
DavidSalomon
October 26, 2006
In Glengarry Glen Ross, Alec Baldwin plays the character Blake, almost earning Baldwin an Oscar for the role. The salestalk presented is one of the finest ever, allthough sarcastic, it contains the foundations of a well meditated salesmen.
   
Google Books
22 Keys to Sales Success:
How to make it big in financial services
By James M. Benson and Paul Karasik
New York, NY: Bloomberg Press
2004
Pg. 127 (KEY 16: Always Be Closing):
THE PRIMARY ADAGE IN SELLING HAS BEEN, AND ALWAYS WILL be, ABC: Always Be Closing.