Rubber Arm (1910)

“Manager Donovan thinks very highly of [Louis] Leroy, as he is a strong and willing worker. He has what is called a ‘rubber’ arm, as he is ready to go in at any time when he is needed.” Montpelier Morning Journal, January 13, 1910, p6

“(Bob) Steele is a southpaw with what is called a ‘rubber arm.’ He seldom tires.” Washington Times, March 20, 1916 p11

“WIth the Yankees he [Allan Russell] earned the name of Rubber Arm because he could pitch any time he was called on without regard to the time he had had to rest.” Boston Globe, July 18,1918 p7

Earlier examples with other usage:

  1.  Strong throwing arm
    “Ward then tried to steal second, but Ewing brought his new rubber arm into play, and it sent the ball like a rifle shot to Fuller at second, cutting Ward off….” Brooklyn Daily Eagle, August 11, 1892, p2. 
  2. Ability to throw curve ball
    “Rubber arm of a farmer. Brown’s twisters fooled the Barons badly. (Headline) Buffalo Courier, June 6, 1897, p14
    “Sam Leever’s ‘India Rubber’ arm.” (Headline). “The professor keeps his arm soft and pliable ‘on purpose’ by a system of massage, for that’s his idea of an arm in condition for throwing the most deceptive curves.” Fort Wayne Daily News, September 24, 1903, p7
  3. Ability to extend reach to make a catch
    “Outfielder DeFresne must have had a Rubber Arm.” (Caption on illustration showing outfielder making a great catch). Poughkeepsie Eagle-News, June 10, 1913, p2
    “….at first base he developed an india rubber arm for high throws….” Dayton Daily News, November 30, 1919, p12
  4. Said of a pitcher unable to control his pitches
    “He [Grover Loudermilk, “the human giraffe”] had what is termed a ‘rubber arm,’ and the elastic stuff drove him out of the league. A rubber arm is one which cannot be controlled.” Evening Public Ledger (Philadelphia), June 29, 1914, p14

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1933. “Name given to a pitcher who can work often” (Famous Sluggers and Their Records of 1932).