I agree with Beverly that our schools need to make greater strides in enhancing our ability to serve all children. Unfortunately, in many cases there are, indeed, certain children a school cannot, at present, serve appropriately. At the same time, there are often compelling reasons to accept children whom we know might be better served elsewhere. These reasons range from wealthy donors to enrollment/sustainability issues to other political concerns.
Regardless of the competing concern, I would suggest that the decision to enroll a child must be based first and foremost on what is good for that child. School administrators are under tremendous pressures to provide for the needs of the many, but we can never allow ourselves to sacrifice the best interests of an individual child for the sake of the greater good. Assuming no creative solutions exist, a school faced with this quandary should guide the family towards the school that is in the best interests of the child and pursue funding streams in other manners.
As a follow up, one clarifying question came to mind: the question notes that there is a competing school which excels at serving children of this particular profile. Is that competitor also a Jewish day school? If not, how do we determine whether the child's best interests are truly served more effectively at a non-Jewish school designed to support her learning profile or at a Jewish school which is not an ideal educational fit?