Wolf-Hirschhorn syndrome, caused by a missing part of the short arm of chromosome 4, occurs in about one in 50,000 live births. Disabilities can vary from child to child but can include seizures, hearing loss and eye malformations, as well as kidney, brain and skeletal abnormalities. Heart disease and frequent lung infections and immune deficiencies have also been reported.
Patients can be denied an organ transplant for a variety of reasons, according to the American Society of Transplant Physicians. Transplantation will not be offered to those would could be harmed by the surgery itself or by the immune-suppression that is required to prevent organ rejection.
Patients with weak immune systems or a high risk of infection, such as some children with Wolf-Hirschhorn syndrome, cannot be immunosuppressed, according to those guidelines.
Some doctors have reported that patients with Wolf-Hirschhorn syndrome have difficulty with anesthetics, because their heads and mouths tend to be small, making it hard to place a breathing tube during surgery.
Patients with severe heart disease may have an unacceptably high risk during surgery. Also, those who are not expected to live five years may also be denied a kidney transplant.
Patients with severe intellectual disabilities may be considered for transplant if the benefits outweigh the potential harm, say the guidelines.
Today, Mia cannot yet walk or talk, and has a gastrointestinal tube because she can't eat by herself. "But she smiles and plays and recognizes us and loves her brothers," said Rivera. "They love to play with her.
"Any mother wants the best for her child and will do whatever it takes to get it," said Rivera, "Mia isn't to blame for this. She didn't want or ask for this syndrome, and all we ask for is the right to fair medical treatment."
ABC News' Dr. Elizabeth Chuang contributed to this report.