“The gift that keeps on giving” is a gift that serves the user for longer than just one day (such as a birthday or holiday). “A Gift That Keeps on Giving” was printed in an advertisement for a savings account in Colonial Trust Co. in the Reading (PA) Daily Times on December 1906. “The Gift That Keeps On Giving” was in an advertisement for Scandinavian-American Bank in the Seattle (WA) Sunday Times on December 19, 1909. A bank account “keeps on giving” by earning interest.
   
“The Autopiano—The Gift That Keeps on Giving” was printed in the San Francisco (CA) Chronicle on December 23, 1909. “The gift that keeps on giving—that keeps on giving something new. For no matter what kind of music you may want or when you may want it, a Victrola Instrument and Victor Records give you every kind of music—better” was printed in Better Homes and Gardens magazine in December 1924. The Victor Corporation of America secured a trademark on “The Gift That Keeps on Giving.”
     
“VD: the gift that keeps on giving” was said by host Dick Cavett on the television special V D Blues in October 1972.
   
     
Wiktionary: gift that keep on giving 
Noun
gift that keeps on giving (plural gifts that keep on giving)
1. (US, idiomatic) Something with continuing consequences.
2. (US, slang) A sexually transmitted disease.
         
20 December 1906, Reading (PA) Daily Times, pg. 4, col. 7 ad:
A Gift That Keeps on Giving
Open a savings account for your boy or girl as a holiday gift.
It will be a gift that keeps on giving and that will give the recipient a boost toward independence and wealth.
Safety for savings and 3 per cent.
Colonial Trust Co.
   
19 December 1909, Seattle (WA) Sunday Times, pg. 24, col. 5 ad:
The Gift That Keeps On Giving
(A Savings Book.—ed.)
Scandinavian American Bank
 
23 December 1909, San Francisco (CA) Chronicle, pg. 16, col. 7 ad:
The Autopiano
The Gift That Keeps on Giving
(...)
No gift can compare with the Autopiano. It is the gift that keeps on giving. It gives pleasure and happiness to every member of the family for every day of years to come.
     
Chronicling America
12 December 1910, The Star (Seattle, WA), pg. 4, col. 5 ad:
The Gift That Keeps On Giving
(A Savings Book.—ed.)
Scandinavian American Bank
 
21 December 1911, Anaconda (MT)

, pg. 15, col. 1 ad:
The One Gift That Keeps on Giving
(...)
State Savings Bank
Butte, Montana
 
4 December 1923, Nashville (TN) Tennessean, pg. 11, col. 1 ad:
Gifts That Keep on Giving
For Mother and Daughter
(...) (Carving set, knives, forks, spoons, percolator, etc.—ed.)
Craig & Shoffner Hwd. Co.
 
December 1924, Better Homes and Gardens (Des Moines, IA), pg. 52 ad:
The finest gift of all!
The gift that keeps on giving—that keeps on giving something new. For no matter what kind of music you may want or when you may want it, a Victrola Instrument and Victor Records give you every kind of music—better.
(...)
Victrola
Victor Talking Machine Company, Camden, N. J.
 
Google Books
Hearst’s International
Volume 46
1924
Pg. 168:
The gift that keeps on giving— that keeps on giving something new. For no matter what kind of music you may want or when you may want it, a Victrola Instrument and Victor Records give you every kind of music— better.
 
OCLC WorldCat record
V D blues. A show about syph and clap after which you will know all you need to know about the gift that keeps on giving. Host: Dick Cavett.
Author: Don Fouser; Educational Broadcasting Corporation.
Publisher: New York [Educational Broadcasting Corp.] 1972.
Edition/Format:   Print book : English
 
10 October 1972, Boston (MA) Globe, “Night Watch: An attack on VD—via the funny bone” by Percy Shain, pg. 21, col. 1:
(Review of “VD Blues.”—ed.)
Some of the catch lines from commercials ... “VD: the gift that keeps on giving” ... were alternately amusing or irritating—but they were all attention grabbing—and that was the main idea.
   
OCLC WorldCat record
VD: the gift that keeps on giving.
Author: Copley Productions.; Oxford Films.
Publisher: Copley Productions, Released by Oxford Films, 1973.
Edition/Format:   Film : Film : Secondary (senior high) school   Visual material : English
Summary:
Focuses on the efforts of a group of teenage volunteers who are telling other young people about venereal disease. They are proceeding on the theory that information from members of peer groups is more readily acceptable than information from the establishment.
 
OCLC WorldCat record
Pete’s Christmas : the gift that keeps on giving
Author: Nisha Kumari Ganatra; Zachary Gordon; Molly Parker; Bailee Madison; Bruce Dern
Publisher: [Santa Monica, CA] : ARC Entertainment, 2013.
Edition/Format:   DVD video : English
Summary:
A fourteen-year-old boy named Pete had the worst Christmas Day ever and wakes up to find he must repeat the day again and again until he gets it right.
   
Urban Dictionary
gift that keeps on giving
syphilis, AIDS, gonorrhea, chancroid, chlamydia, hepatitiis, herpes, HIV, HPV, gonorrhea, any disease transmitted by sexual activities (STD). you get it from someone and you can give as many as you want.
you: oh man i gave my GF Gonorrhea
me: the gift that keeps on giving to your next partner
#gift that keeps giving#venereal disease#vinereal disease#std#std#sexually transmitted disease#
by whhatup69 November 11, 2013
 
(Trademark)
Word Mark THE GIFT THAT KEEPS ON GIVING
Goods and Services (EXPIRED) IC 009. US 036. G & S: TALKING MACHINES AND PARTS THEREOF, TALKING MACHINES AND PARTS THEREOF ADAPTED FOR COMBINATION WITH RADIO RECEIVING SETS, AND TALKING MACHINE RECORDS. FIRST USE: 19241128. FIRST USE IN COMMERCE: 19241128
Mark Drawing Code (5) WORDS, LETTERS, AND/OR NUMBERS IN STYLIZED FORM
Serial Number 71207900
Filing Date January 9, 1925
Current Basis 1A
Original Filing Basis 1A
Registration Number 0224081
Registration Date February 15, 1927
Owner
Assignment Recorded ASSIGNMENT RECORDED
Type of Mark TRADEMARK
Register PRINCIPAL
Renewal 2ND RENEWAL 19670215
Live/Dead Indicator DEAD
 
(Trademark)
Word Mark THE GIFT THAT KEEPS ON GIVING
Goods and Services IC 035. US 100 101 102. G & S: Advertising, marketing and promotion services in the field of the recorded music industry. FIRST USE: 20180701. FIRST USE IN COMMERCE: 20180701
Standard Characters Claimed
Mark Drawing Code (4) STANDARD CHARACTER MARK
Serial Number 88028975
Filing Date July 8, 2018
Current Basis 1A
Original Filing Basis 1A
Owner (APPLICANT) VICTOR CORPORATION OF AMERICA CORPORATION NEW JERSEY 6713 RUDDEROW AVE. Pennsauken NEW JERSEY 08033
Type of Mark SERVICE MARK
Register PRINCIPAL
Live/Dead Indicator LIVE