Fiat was founded in 1899 in Turin, Italy. “Fiat” is an acronym for “Fabbrica Italiana Automobili Torino.” However, Fiat vehicles have been nicknamed with the backronym (back acronym) “Fix It Again, Tony” since at least 1982.
 
The “Fix It Again, Tony” nickname and Fiat’s perceived problems were so great that Fiat left the U.S. market in 1983. Fiat began purchases into Chrysler in 2009.
 
   
Wikipedia: Fiat
Fiat S.p.A. (Fabbrica Italiana Automobili Torino, Italian Automobile Factory of Turin) is an Italian automobile manufacturer based in Turin. Fiat was founded in 1899 by a group of investors including Giovanni Agnelli. During its more than a century long history, Fiat has also manufactured railway engines and carriages, military vehicles, farm tractors, and aircraft. As of 2009, the Fiat group (not inclusive of its subsidiary Chrysler) was the world’s ninth largest carmaker and the largest in Italy.
 
Fiat-based cars are built around the world. Outside Italy, the largest country of production is Brazil, where the Fiat brand is the market leader. The group also has factories in Argentina and Poland and a long history of licensing production of its products in other countries. It also has numerous alliances and joint ventures around the world, the main ones being located in Italy, France, Turkey, Serbia, India and China.
 
26 October 1982, The Times-Picayune (New Orleans, LA),  “‘America Fights Back’: Quality is Detroit’s theme for ‘83” by Paul Perret, sec. 3, pg. 2, col. 6:
Fiat’s reputation for quality and reliability has become so bad that many owners say the name means “Fix It, Again Tony.”
 
15 February 1983, The Morning Union (Springfield, MA), “Happy goodbye to automaker leaving the U.S. market” by Stephen Chapman, pg. 15, cols. 3-4:
But of several dozen Fiat owners I’ve met, none would ever buy a second one. They’re the ones who spread the old joke: Fiat stands for “Fix it again, Tony.”
 
Google Books
Reinventing the Wheels:
Ford’s Spectacular Comeback
By Alton F Doody and Ron Bingaman
Cambridge, MA: Ballinger Pub. Co.
1988
Pg. 5:
The very name “Fiat” was sarcastically translated as an acronym for “Fix it again, Tony.”
 
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The Secret Empire:
How 25 Multinationals Rule the World
By Janet Lowe
Homewood, IL: Business One Irwin
1992
Pg. 77:
The company’s reputation in the United States for cars that needed frequent, costly repairs (hence the epithet, Fix It Again Tony) forced Fiat eventually to withdraw from the U.S. market.
 
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Comeback:
The Fall and Rise of the American Automobile Industry
By Paul J. Ingrassia and Joseph Blanco White
New York, NY: Simon & Schuster
1994
Pg. 204:
In the summer of 1989 he had stopped in Rome to have lunch with Giovanni Agnelli, the chairman of Fiat. In 1983 Fiat had pulled out of the U.S. market — where its shoddy quality spawned the joke that the company’s name stood for “Fix It Again, Tony” — but Agnelli was a formidable force.
 
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Lemon-Aid Used Cars and Trucks 2010-2011
By Phil Edmonston
Toronto, Ont.: Dundurn Press
2010
Pg. ?:
The company couldn’t overcome the public’s perception that Fiat stood for “Fix it again, Tony.” Now, more than 25 years later, that perception has been confirmed by low scores on J.D. Power and Associates’ 2008 Customer Satisfaction Index studies for France, Germany, and the United Kingdom.