In all the cases I know of, I think the family was either not-Frum or not-so-Frum at the time. I would guess that in the majority of cases in which the family is Frum, the kids do choose to be Jewish. And if the family isn’t Frum, it probably doesn’t matter so much if the kid isn’t Jewish.
Either way, they probably continue to love their kid because he is their kid. Just like a Ger loves his kids because they are his kids even though he is Jewish and they aren’t. In this case, it is probably harder because the kid is rejecting the values and lifestyle that his family raised him with.