The mother isn’t actually being treated in this case; she is deceased. Deceased bodies can receive “support” (to be distinguished with “life support”) for certain reasons, such as for various organs to remain viable for transplant. It cannot go one forever, though; the body starts to decay, albeit at a slower rate than if no support is provided.
With regard to the main issue of this thread, it is simply a sad state of affairs. The mother is deceased. The natural course of events is that the baby dies also. It is only through massive, unnatural intervention that this can even be an issue. If it is done for a short time, it might be possible for the baby to remain viable. But when it goes on for weeks or months on end, I’m not so sure.
The fetus normally receives information from the mother, which we fully don’t understand the benefits of yet. The fetus obviously is receiving little, if any, such information at this point. Also, during a normal pregnancy, the mothers body is geared toward survival of the fetus (immune system adjusts, etc.). Since the mother is not longer alive, this is no longer the case. And since the body is slowly decaying, we really have not idea how badly this will affect the fetus.
I’m all for helping the baby; and ultimately it is up to the medical professionals to decide. But man has his limits, and it appears in this particular case that the baby is ultimately an experiment, so see how long the baby survive in a dead mother. Some things were not meant to be, and we should not play God.