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You can use kitten milk until you can get some puppy formula for the little guy. Goat's milk is also a good substitution as it is closest to a dog's milk. However, while you are attempting to substitute formula, try putting a little smear of karo syrup or pancake syrup on your pup's tongue so he gets the little boost of energey and the taste. Then remove the other pups and put a smear on one of mom's nipples. Then try to get the pup to nurse from mom. Often the smell of the syrup and the taste will get a pup nursing off of mom which is a better choice in the long run. Also I am assuming since you have kitten formula that you are used to bottle feeding. I wanted to add that some people will put an unused makeup sponge in the nipple to keep the flow of formula regulated so it isn't aspirated into the lungs. Many breeders forgo nipples all together and let pups suck on the sponge itself but you have to keep an eye on the sponge and replace with the first sign of any signs of wear to the sponge.
Be sure the whelping area is at least 90F or a little warmer and there are no drafts. It can be rough on us humans but pups can't regulate their own body temperature and need to in a hot environment. Each week the temperature can be reduced by 5 degrees and after 3 weeks they can regulate their own body temperature.
Pups can die for numerous reasons including serious worm infestation, flea infestation causing anemia, herpes virus, and bad milk from mom or congenital health issues. It is sometimes referred to as fading puppy syndrome. Some newborns just don't make it and it is something breeders have to learn to deal with. This site has information on fading puppy syndrome.
You can read about herpes here:
This site goes over ways of helping save fading puppies.
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