Certainly such a thing is quite rare, and I was only asked once for such a thing, but even so, no one was asking for communion for the dying infant; it was for the other members of the family. I had the sense that the motivation for the request was because of a desire of the family members to feel "as one" with the baby.
It's been my experience that in such situations as death - and especially from those present who are not dying - almost anything might be requested. That's not to say that it should be granted; only that at such emotional times almost anything can "come up".
Dear Religion Moderator,
"That's not to say that it should be granted; only that at such emotional times almost anything can 'come up'."
Hmm... I'm sure you're right. I don't have much experience being nearby when folks are dying.
As my mother lay dying last year, we were concerned to make sure she received last rites from her priest, and when it was clear she had died, we read prayers for the dead at her body. I wouldn't know to do something else.
sitetest