“Old soldiers never die—they just fade away” is an old saying that was popularized by General Douglas MacArthur (1880-1964) in his farewell address to Congress on April 19, 1951. Many parodies of the saying have been made.
 
“Old golfers never die—they just lose their balls” is a jocular one-line saying that has been printed on T-shirts. The golf one-liner has been cited in print since at least 1954.
 
“Old golfers never die—they just lose their drive” has been cited in print since 1976. 
 
 
24 June 1954, Lowell (MA) Sun, “The Lookout” by George McGuane, pg. 22, col. 1:
A sign in a golf club read, “Old Golfers never die. they just lose golf balls.”
 
17 June 1964, Arcadia (CA) Tribune, “Along The Mazdas: with DeMuth, pg. 5, col. 3:
SIGHTS AND SOUNDS: Overheard at Bob Corral: “Old golfers never die, they just lose their balls.”
 
20 June 1965, Lowell (MA) Sunday Sun, “Do Women Dress for Golf?” by Nancy Scannell, pg. 37, cols. 3-4:
Others are more subtle and just have “Old golfers never die, they just lose their golf balls.”
   
Google Books
The Running of Beasts
By Bill Pronzini and Barry N. Malzburg
Naples, FL: Speaking Volumes, LLC
1976
Pg. ?:
Over the backbar and on the walls were a series of wooden plaques with cartoon drawings and puke-cute sayings like OLD GOLFERS NEVER DIE, THEY JUST LOSE THEIR BALLS ...
 
Google Books
Golfer-at-large:
New Slants on an Ancient Game
By Charles Price
New York, NY: Atheneum
1982
Pg. 14:
Behind the bar will be a wood plaque on which is printed the hilarious observation that old golfers never die, they just lose their balls.
   
Yotta.com
From: .(JavaScript must be enabled to view this email address)
Newsgroups: rec.humor
Subject: Canonical List of Old * Never Die, they just ...
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Distribution: world
Organization: top down of course
 
Canonical Lists of Old * Never Die, they just ...
=================================================
Revised: 15 January 1996
(...)
OLD GOLFERS never die, they just lose their balls
OLD GOLFERS never die, they just lose their drive
   
Google Books
The 19th Hole:
Stories and Yarns from the Fairways
By Bernard Gallacher
London: Chameleon
1996
Pg. ?:
He was recovering from an illness, and friends sent the usual get well cards, one of which said “Old golfers never die, they just lose their balls.”
 
Google Books
Behold the Proverbs of a People:
Proverbial Wisdom in Culture, Literature, and Politics
By Wolfgang Mieder
Jackson, MS: University of Mississippi Press
2014
Pg. ?:
The proverb has given rise to a cycle of parodic jokes, which are antiproverbs (“Old doctors never die, they just lose their patients”; “Old golfers never die, they just lose their balls”).