No clear explanation has been given. However, although Jack's blood doesn't make him immortal, it is "immortal blood" (as it was termed several times). There must be something about it to which the Blessing reacts, even though nobody knows what that "something" is. Nobody knows, either, just what the Blessing is or how it works, which doesn't help when seeking explanations.
It was repeatedly said that there was nothing special about Jack's blood but that just means that none of those who examined it could find anything special about it. Their technology wasn't able to detect the "something" that the Blessing could detect.