"The brave don’t live forever/long, but the cautious don’t live at all” (or “Brave men don’t live forever...") is a saying that has been printed on posters. The saying is sometimes credited to Timothy Luce, but he graduated from college in the 1990s and could not have originated it.

“Brave men don’t live forever — but the cautious don’t live at all” was cited in 1989, when the saying had been printed on a wooden plaque. “The brave may not live long, but they go their way with a splendor and a dignity, and men talk about them when they have passed by” was written in 1937 by New York City sportswriter Jimmy Cannon (1909-1973).


16 May 1937, Oakland (CA) Tribune, “Cohn-ing Tower” by Art Cohn, pg. 10-A, col. 1:
“The brave may not live long, but they go their way with a splendor and a dignity, and men talk about them when they have passed by. Such a man is Bob Pastor.”
(Written by New York City sportswriter Jimmy Cannon—ed.)

Google Books
2 Wheels to Adventure:
The first overland journey from Alaska to Argentina
By Danny Liska
Niobrara, NE: Bigfoot Pub. Co.
1989
Pg. 205:
When l stepped into his home and saw the wooden plaque on the mantel, l liked him immediately; it read: “Brave men don’t live forever — but the cautious don’t live at all.”

Google Books
Your Home Computer:
From Novice to Master
By Jessie Strahan withMike Lindelsee
Coronado, CA: Misty World Pub.
2000
Pg. 79:
“The brave don’t live forever, but the cautious don’t live at all”
Timothy Luce

Google Books
First Year, Worst Year:
Coping with the unexpected death of our grown-up daughter
By Barbara A. Wilson and Michael John Wilson
Hoboken, NJ: John Wiley & Sons, Inc.
2004
Pg. 135:
The card said: The brave don’t live long but the cautious don’t live at all. Here’s to the brave.

The Internet Movie Database
Survivor: Season 11, Episode 3
The Brave May Not Live Long, But the Cautious Don’t Live at All (29 Sep. 2005)

Twitter
Jared Banares‏
@jaredbanares
“The brave don’t live forever, but the cautious don’t live at all.” - Timothy Luce http://tumblr.com/xlo2f6nzb
6:12 PM - 21 Jul 09

Daily News (New York, NY)
‘The Crash Reel,’ TV review
Plenty of pain, little gain for athlete victims in HBO’s documentary about high-risk sports
By David Hinckley
Monday, July 15, 2013, 2:00 AM
(...)
Pearce himself, before and after the injury, says he can’t imagine anything close to snowboarding for sheer exhilaration. A TV commentator recites the old line that “the brave may not live long, but the cautious don’t live at all.”