Euthanasia is never acceptable for a severely ill infant. The infant is not able to talk or make a decision, and should not be put down just because the infants is severely ill.. Technology has come a great way and miracles happen all the time, so you never know if the infant will pull through.
As a personal anecdote, I was a severely ill infant. I required medical attention for about a year and since, I have been a really healthy person. To simply end a life early because it may be difficult for a year or more removes the possibility that people's lives may get better. Also in the day of 21st century medicine, one should be able to help infants with their diseases.