The woman, who was 29 when she had her second ovary taken out for medical reasons, continues to rely on hormone replacement therapy (HRT) nine months after her ovary tissue was returned.
When surgeons announced last February that they had performed the procedure for the first time, they said it would take until November at the latest to determine if the ovarian tissue was fully functional and producing hormones.
They have admitted now that although the ovary appears to have grafted well, it has failed to ovulate naturally and produce enough hormones for the patient to end her HRT treatment.
But scientists emphasised that the operation was only an experimental procedure on a "less than ideal" patient and they are confident that they can induce ovulation in a transplanted ovary using drugs.
News of the operation was hailed with headlines claiming "the menopause is reversed".
The operation raised the prospect of young professional women "banking" their ovaries so they could have them returned after establishing their careers. This would keep their eggs more youthful and increase the chances of having babies in middle age.
The patient, Margaret Lloyd-Hart, who is now 30 and lives in Arizona, United States, is a professional dancer. Doctors believe that her rigorous exercise regime may have interfered with the ability of her ovary to trigger regular menstrual cycles.
Kutluk Oktay, director of reproductive endocrinology and infertility at New York Methodist Hospital, where the transplant took place, said that the operation has been technically a success.
The transplanted tissue produces ovarian follicles - fluid-filled blisters in which eggs develop - although they fail to burst to release the egg and female hormones, he said.
"In a situation like this, given the circumstances, I would consider it a success from a scientific point of view. She's happy with the fact that the ovarian functions have returned but she has not completely achieved her goal in terms of her menopausal symptoms that she wanted to cure because she still needs to take the hormones," Dr Oktay said.
"In terms of her mood and other symptoms, she is not completely relieved of them, but she's happy with the situation that gave her an added option regarding her future fertility," he said.
Dr Oktay, who initially collaborated with Professor Roger Gosden, formerly of Leeds University and now at McGill University in Montreal, Canada, said that undue emphasis has been placed on using ovary transplants to reverse or delay the menopause.
"The main purpose is to create a reproductive option for young cancer patients who would otherwise be sterilised through radiation or chemotherapy," he said.
Mrs Lloyd-Hart is due to fly to New York shortly for further tests, but Dr Oktay said that if the ovary was to have started producing hormones as it should, he would have expected it to do so by now.
A few months ago, Mrs Lloyd-Hart was given an injection of drugs to induce her ovary tissue to ovulate, but this has not occurred naturally - a crucial measure of the success of the transplant.
"There are different shades of success. The importance of this case study is proof of the principle that a procedure like this can work and frozen banks of ovaries can produce eggs. It paved the way to further studies with better candidates," Dr Oktay said. "I believe we are at the beginning of a process that may take 10 years, but at the end of 10 years we might be looking at quite a routine procedure."