You need to do a health check as soon after birth as possible. Demons any afterbirth, bloody hay, dead kits. Also count the babies and look them over carefully for any genetic defects (cleft palette, hernias, etc).
If they don't have full milk bellies, I put them back with the doe, otherwise I keep them until sunrise/sundown and return for nursing while I check/feed the other rabbits, then take the nest box back inside. Nursing only takes about five minutes and the doe will be back outside the nest box. By taking the nest box inside, I can catch any kits that were dropped outside the box before they get too chilled!
Now, inside, I actually move the litter(s) into baskets lined with towels and as I walk by during the day, I stir the babies and get them acclimated to my touch/smell. This makes a difference in how many end up being spastic little babies later on. LOL