The heart has its own internal pacemaker (think of it like a battery pack for a laptop). With artificial respiration the heart continues to receive oxygen so the heart can continue beating after brain death, but without input from the brain, it will eventually stop even with artificial respiration, typically the heart can be kept beating in a brain dead person on a ventilator, but for not much longer than a month, although most people who have been verified to be brain dead are taken off life support by or before then so it is unclear how long the heart can be kept beating in a brain dead person while on vent.
Given a supply of oxygen the human heart can even be kept beating outside of the human body for a time. This is what makes heart transplants possible. During some open heart surgeries, the older techniques, the heart is stopped and partially removed from the body and the patient is put on heart-lung bypass machine to do the work of the heart during surgery. The patient is not however brain dead and not dead even though their heart has stopped beating.
Without any input from the brain however, the body will cease secreting hormones vital for maintaining organ and other biological functions including gastric (stomach and bowels), kidney and immune functions and regulation of blood pressure and temperature. Sometimes a person who has been pronounced brain dead and consented or their family has consented to organ donation, will not only be kept on a ventilator but also given hormones and kept under heated blankets to keep their organs viable and give the family a bit more time to day their goodbyes, but that typically is only for a few days.
Life After Brain Death: Is the Body Still 'Alive'?
This (complete brain death, including that of the brain stem) is very different from traumatic brain injury or a PVS or coma in that in those patients; parts of the brain and more precisely the brain stem is still functioning, regulating and maintaining biologic functions. In the case of Terri Shiavo (and Karen Ann Quinlan for that matter), she had loss of some but not all brain function. She was able to breath and move on her own, had eye movement and because her brain was still regulating other biologic functions, this is why she was able to be fed through a feeding tube, why she was still able to digest and utilize nutrition, regulate her core body temperature and fight off infection.
It is unclear in Jahi’s case if her internal organs, other than her heart, are still functioning at this point and why a feeding tube is very likely futile and may even hasten her bodily deterioration as insertion and maintenance of a feeding tube has a high risk of infection and pumping nutrition directly into the stomach of a person who’s gastric system is likely no longer functioning, is probably why Children’s Hospital, and no doctor the family contacted, wanted to perform the procedure.
I’m not sure if the link will work, but I will put it here anyway.
http://link.springer.com/article/10.1007%2FBF01400587#page-1
Looking at the figures in the article, it appears that the longest they have kept a corpse somewhat functional after death is about 52 days.
This group, led by T. Yoshioka of Osaka University Medical School, Japan, apparently has done a number of studies in brain dead people.
In any case, I doubt that the heart will continue to beat in this corpse for much longer. Almost certainly, whatever facility they moved her to will not have advanced life-support equipment. The length of time this corpse has been kept ventilated is already beyond the average seen in Yoshioka’s studies (23.1 +/- 19.1 days) (http://www.ncbi.nlm.nih.gov/pubmed/3714004).
The judge who has allowed this travesty to continue long past the girl’s death is reprehensible. I have no words to describe the lawyer Dolan, who must be aware of the facts yet continues to lead the family on.
I think there will be severe legal ramifications in this case. Hospitals do not usually release corpses except for transport to medical examiners or funeral homes.