“A diplomat is a man who always remembers a woman’s birthday but never remembers her age” (or “...but forgets her age”) is a jocular saying that has been cited in print since at least 1913. The saying has often been attributed to American poet Robert Frost (1874-1963) since at least 1949, but there’s no evidence that Frost either coined or popularized the saying.
 
   
Hathi Trust Digital Library
2 August 1913, Implement Age (Springfield, OH), pg. 26, col. 1:
Tommy—Pop, what is a diplomat?
Tommy’s Pop—A diplomat, my son, is a man who remembers a woman’s birthday but forgets her age.
 
Hathi Trust Digital Library
September 1913, The School Journal, pg. viii, col. 2:
Tommy—Pop, what is a diplomat?
Tommy’s Pop—A diplomat, my son, is a man who remembers a woman’s birthday, but forgets her age.—Philadelphia Record.
 
Google Books
December 1913, The Square Deal, pg. 470, col. 2:
Diplomacy.
Tommy.—“Pop, what is a diplomat?”
Tommy’s Pop.—“A diplomat, my son, is a man who remembers a woman’s birthday, but forgets her age.” — Brooklyn Citizen.
 
28 April 1914, Denver (CO) Post, pg. 4, col. 8:
“What’s a diplomat?”
“A diplomat is a man who remembers a woman’s birthday, but forgets her age.”—New York American.
 
Google News Archive
1 October 1915, Neppel (WA) Record, pg. 5, col. 4:
Correct.
“What is your idea of a real diplomat?” asked the old fogy.
 
“A real diplomat is a man who always remembers a woman’s birthday and always forgets her age,” replied the grouch.
 
Google News Archive
19 March 1922, The Telegraph-Herald (Dubuque, IA), “Sunday Shorts” by Lane Orrick, pg. 15, col. 2:
The real diplomat remembers a woman’s birthday and forgets her age.
   
Google Books
A Connotary;
Definitions not found in dictionaries, collected from the sayings of the wise and otherwise
By John Garland Pollard
New York, NY: Thomas Y. Crowell
1935
Pg. 31:
Diplomat — A man who remembers a woman’s birthday and forgets her age.
   
9 September 1949, The Daily Journal-Gazette and Commercial-Star (Mattoon, IL), pg. 8, col. 6:
“A diplomat is a man who always remembers a woman’s birthday, but never her age.”—Frost.
 
Google Books
Speaker’s Handbook of Epigrams and Witticisms
By Herbert V. Prochnow
Blackpool: A. Thomas & Co.
1955
Pg. 29:
A diplomat is a man who always remembers a woman’s birthday but never remembers her age. Robert Frost
 
GoogleNews Archive
7 May 1956, Spokane (WA) Daily Chronicle, pg. 1, col. 1:
FOOD FOR THOUGHT
Robert Frost once said that diplomat is a man who always remembers a woman’s birthday but never her age.”
 
Google Books
The Concise Columbia Dictionary of Quotations
By Robert Andrews
New York, NY: Columbia University Press
1989
Pg. 79:
A diplomat is a man who always remembers a woman’s birthday but never remembers her age.
Robert Frost (1875-1963)
American poet