The second transplant, also of adult lungs, involved "high-risk" organs because they were infected with pneumonia, she said.
Children's Hospital continued its policy of refusing to comment on the case.
Sarah's mother and father, Fran, said the first lungs failed because of a complication called "primary graft failure" that occurs in up to one-quarter of cases and that is often fatal. Basically, the lungs fail to function when blood flow resumes after surgery.
Graft failure can occur in lungs that appear to be high quality, but in this case, Janet Murnaghan said, the lungs were "known to be in less-than-optimal condition."
Sarah was placed on a machine that took over the function of her heart and lungs until the second transplant.
Position on the transplant waiting list is based on severity of illness, and Sarah's condition was so dire her family was told she could survive no more than a week. The Murnaghans and Sarah's medical team accepted the high-risk lungs because they were considered Sarah's "best and only hope."
"Her surgeon said it's a miracle she's here at this point," her mother said.
Although Sarah cannot speak because of the ventilator tube in her throat, she is alert and communicating by pointing to things, her mother said. She was shocked to learn she had undergone a second transplant.
According to the United Network for Organ Sharing (UNOS), 43 transplant patients in 2012 received a second transplant within seven days of the first transplant, out of more than 20,000 transplants. Most of those were livers; none were lungs.
In 2010 and 2011, UNOS said, seven lung-transplant recipients got a second transplant soon after the first. From 2010 through 2012, 42 lung-transplant patients - less than 1 percent - got a second set of lungs within six months.
Sarah, who has cystic fibrosis, still faces a grim prognosis. Studies show the chances of surviving a year are dramatically reduced by factors that include being on a ventilator before transplant, suffering graft failure, and undergoing a second transplant.
On Monday, Sarah must undergo yet another procedure to "flatten" her diaphragm and, it is hoped, improve its function, her mother said. Her diaphragm is partially paralyzed, which is why an attempt to take her off the ventilator Wednesday was unsuccessful.
Murnaghan said she felt "exhausted" and "beaten up." She and her husband have been at the hospital continuously for weeks; their three other children have been staying with her sister.
"It's been harder than Sarah expected. Harder than I expected," she said.
Sarah waited 18 months for children's lungs before her family went to the media and political leaders for help and filed a lawsuit to have her placed on the adult-transplant waiting list. They said that would give her a fairer chance at getting a transplant because so few children's lungs become available.
A Philadelphia judge intervened, and Sarah was listed for child, adolescent, and adult lungs.
Sarah's parents have said their goal is to celebrate her 11th birthday at home on Aug. 7.
Contact Stacey Burling at 215-854-4944 or firstname.lastname@example.org.