This is a difficult case.  I would air on the side of parental rights; this isn't that much different than the Lorenzo Odoni case.  However, I would also argue that the parents would have the right to take their child off the ventilator as well if they thought that improvement was impossible and the quality of life was low.  And of course a guardian should be appointed by the courts to make sure that the parents aren't abusive.

Pro-life people are in favor of using the courts to advance these sorts of situations when the person or relatives want to discontinue life support.  The Schiavo case comes to mind.  (Of course, the one caveat with that case is that Terri Schiavo's husband was an awful person and likely an abusive spouse.)