I don't think mom will hurt the chick, but if it can't keep up, eventually I think it will go cold - mom might nest in a different corner of the cage with the other chick. She might return at the sound of the peeping of the chick the first 5 or 15 or 40 times, but at one point the chick is likely to be tired and the peeping too weak and mom might not respond.
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In my experience, the weak chicks die on their own within a week. I've never had a chick that had appeared weak at one point survive longer than that. I've also never had a chick die once it hit the 1-week mark. But my buttons are outside in a small aviary, so they have a lot of room for the chicks to get lost in and the temperature is usually lower than inside temperatures, so they can't handle being away from the parents for very long. So it might be different in your case. My fingers are crossed for the little fellow, at least.