Desir had heart disease. She died of natural causes, medical examiner's office spokeswoman Ellen Borakove said Sunday.
Desir said she was not feeling well and was very thirsty on the Friday flight from Port-au-Prince.
Antonio Oliver, a cousin who was traveling with her and her brother Joel said a flight attendant gave her water.
A few minutes later, Desir said she was having trouble breathing and asked for oxygen, but a flight attendant twice refused her request, Oliver said Sunday in a telephone interview.
After the flight attendant refused to administer oxygen to Desir, she became distressed, pleading, "Don't let me die," Oliver recalled.
Other passengers aboard Flight 896 became agitated over the situation, he said, and the flight attendant, apparently after phone consultation with the cockpit, tried to administer oxygen from a portable tank and mask, but the tank was reportedly empty.
Two doctors and two nurses were aboard and tried to administer oxygen from a second tank, which also was empty, Oliver said.
Desir was put on the floor, and a nurse tried CPR, to no avail, Oliver said. A "box," possibly a defibrillator, also was applied but didn't function effectively, he said.
"I cannot believe what is happening on the plane," he said, sobbing. "She cannot get up, and nothing on the plane works."
Oliver said he then asked for the plane to "land right away so I can get her to a hospital," and the pilot agreed to divert to Miami, 45 minutes away. But during that time, Desir died, Oliver said.
"Her last words were, 'I cannot breathe,"' he said.
Desir, 44, was pronounced dead by one of the doctors, Joel Shulkin, and the flight continued to Kennedy International Airport without stopping in Miami, with the woman's body moved to the floor of the first-class section and covered with a blanket, Oliver said.
American Airlines spokeswoman Sonja Whitemon wouldn't comment Sunday on Oliver's claims of faulty medical equipment. Shulkin, through his attorney, Justin Nadeau, declined to comment on the incident out of respect for Desir's family.
American Airlines, a unit of AMR Corp. and based in Fort Worth, Texas, is the largest domestic airline.