When my husband was an intern, there was a case where an elderly man was on a ventilator. He had no brain activity, and the hospital wanted to take him off life support (and we're not talking food and water here - we're talking ventilator). The poor old man was so far gone that parts of his body were actually starting to, er, um, return to the elements, not to get too graphic. Still, his family wanted to keep him on life support. I don't recall what the outcome was, but I think that eventually the hospital was able to persuade the family that their loved one wasn't coming back, and that keeping him on a ventilator wasn't in his best interest.
Yes that was a point I was incapable of making. My head and my tongue are not jiving right now.
That chance of this baby being able to come off the machines is extremely small. This is a point where the hospital knows there is no hope, and have decided to let nature take it course. The mother is not yet ready to let go, and I can't say I blame her, and she's clinging to hope.