Mandy and Paul Barnett renewed their appeal for more bone marrow donors to come forward after their daughter took a sudden and worrying turn for the worse.
Speaking from Molly-Ann's hospital bedside, Mr Barnett pleaded: "We only need one person – surely that person is out there somewhere."
Time is running out for the six-year-old. Molly-Ann must have a bone marrow transplant within six weeks but her tissue type is very rare and no donor has yet been found.
Hundreds of people across the region have already come forward to offer blood samples to try to find a match.
And This is Hull is today launching a unique online pledge to encourage more people to donate blood in the hope of saving Molly-Ann and children like her.
Surgeons were called into see Molly-Ann yesterday after her condition suddenly deteriorated. The brave youngster has developed a worrying swelling behind her eye which has been causing both her parents and medical staff concern.
The swelling is also proving painful for Molly-Ann who was today wearing an eyepatch over the affected eye. However, surgeons decided she was too weak to undergo an investigative operation yesterday and instead she will have a CT scan of her head to try to determine the cause of the swelling.
Mr Barnett said: "Molly-Ann is fighting an infection at the moment, but she is coping.
"The doctors have told us they want to do a bone marrow transplant after her next chemotherapy session.
"This will take place in about two-and-a-half weeks time and will last around four weeks, so we are looking at the beginning of September when we need the transplant.
"Time is really against us now because it takes around four weeks to process samples.
"So if anyone can help Molly-Ann they will need to give a sample within the next 1 week."
Molly-Ann was diagnosed as having acute myeloid leukaemia last September.
She has undergone five courses of chemotherapy each lasting about a month.
Mandy, 40, and Paul, 43, of Hessle, who also have a son Daniel, 18, and another daughter Nikki, 16, are desperate to stress that time is of the essence.
Mr Barnett added: "Just keep on donating. We are only looking for that one person and we know that person is out there.
"We will get there, there is a match for Molly-Ann we just need to find it.
"The response has been absolutely tremendous and we hope people will continue to help us."