Argentina, who have reached four finals - including three since 2006 - must play off against as yet unknown opponents to retain their world group status having been upset by Italy in the first round in Mar del Plata two weeks ago.
"It's necessary to make deep changes to correct mistakes that have been repeated for so many years," said world number five Del Potro, who does not see eye-to-eye with team captain Martin Jaite.
Del Potro also reacted to rumours and erroneous reports after the Italy defeat suggesting he would only play for Argentina under certain conditions.
"I won't permit my name to be used to justify resignations that will only paper over the cracks. I never asked for a (specific) captain and always respected others' decisions even if they didn't respect me," he said in a letter to the AAT.
"Out of consideration for the people who follow me, who enjoy tennis... and know what I've done in the Davis (Cup) and Olympic Games... and are a long way from insulting rivals or punishing someone from their country, I won't play the Davis Cup for the rest of 2014."
Del Potro, Olympic bronze medal winner at the 2012 London Games, has been unhappy with attitudes towards him from some corners of the AAT and media since being made a scapegoat for Argentina's unexpected defeat in the 2008 final at home to a Spain team missing Rafael Nadal.
The 2009 U.S. Open champion dislikes the soccer-type support from sections of the crowd at home matches who question players' commitment to the team if they put their careers on the ATP circuit first, failing to accept their prerogative to do so.
AAT president Arturo Grimaldi said he was surprised by Del Potro's letter and would like to know what his grievances are.
"I'd like to get together with Del Potro and talk with him. People forget what he's done for Argentina," Grimaldi told TyC Sports. "There must be a failing on our part."
Del Potro last played for Argentina in their Davis Cup semi-final loss at home to the Czech Republic in Buenos Aires in 2012. He opted out last year when Argentina also lost to the Czech holders away in the semi-finals.
Argentina reached the final in 1981 thanks mainly to Guillermo Vilas but were defeated away by the United States.
In recent years they have relied heavily on the now retired David Nalbandian but lost the 2006 final to Russia in Moscow and the 2011 final again to Spain in Seville.