As a warning, Bill, “donate it to me” is not an appropriate answer.—LH
You wound me, Lanette. You wound me. —Bill
Unfortunately, this means you’ll need to care for the puppy yourself. It’s very rare (and difficult) to get the mother to adopt her pup after she’s rejected it, and in some cases, she may even attack the puppy if you try to reintroduce it.
That having been said, there are three things you need to monitor for immediately after birth if you haven’t figure it out already: hypothermia, low blood sugar, and dehydration. If your puppy is shivering, that’s a good thing. If it isn’t and if its nose is losing color, that would be hypothermia. If your puppy’s nose and gums are wet, then it’s fine, but if you feel a sticky, mucous membrane in its mouth, then dehydration is setting in. Finally, if your puppy is more lethargic than usual or if it’s convulsing, then its blood sugar is dangerously low. The latter two conditions warrant a trip to your local pokémon center, but it’s important to know that there are ways to prevent your eevee from getting to this state.
First, heat. It’s important to stabilize your eevee’s body temperature within the first week. Use heat lamps and hot water bottles to keep your eevee warm; blankets shouldn’t be used in addition to this, as it’s very easy to induce heat stress in your puppy (which is just as bad as hypothermia … just less difficult to achieve). Try to keep your eevee’s environment at around 86 degrees Fahrenheit (30 degrees Celsius) on the first two days, then drop the temperature down by a degree each day after that until your eevee can survive on its own body heat.
Feeding, meanwhile, is a bit more difficult to resolve, but it’s vital for not only the other two issues I’ve mentioned above but also the development of your eevee’s immune system. If you have another female mammalian pokémon that’s of breeding age, try to get it to nurse from her. If not, try to find a breeder or a friend with one such pokémon and ask them for milk, or purchase raw miltank milk or specially crafted eevee formula. The latter may be the easiest option, actually, as it’s readily available at all pokémarts and contains all the vitamins, minerals, and sugars a growing eevee needs. It just doesn’t quite provide the biological component that helps with a young eevee’s immune system, so some trainers prefer the more organic method if they can find it.
All young eevee need to be fed about once every two to three hours. (If it’s healthy, it will cry to let you know when it’s time.) If not feeding from another pokémon, you’ll need to give it its milk or formula from a bottle. Be sure to sterilize the bottle before loading by boiling it for five to ten minutes in water. Dry thoroughly, then fill it. Finally, warm the bottle gently until it reaches a temperature of 95 to 100 degrees Fahrenheit (35 to 37.8 degrees Celsius)—or human body temperature, in other words. If a drop of it applied to the back of your wrist is too hot for you, then it’s too hot for your eevee.
Once your eevee reaches about two to three weeks, you can begin to wean it. Feed it milk in a flat dish to teach it how to eat from a bowl for the first two weeks, then give it specially made eevee puppy kibble (available at any pokémart) in addition to the milk for the next two. Decrease the amount of milk you give it each day after you begin feeding it solid foods. After a month, you can switch completely to the kibble and water. (Do not feed it anything but kibble until about two months.)
Finally, one last thing not that many people think of: getting it to relieve itself. Eevee don’t really know this at birth; rather, their mothers lick their stomachs to get them to go. You can simulate this behavior by rubbing your eevee’s stomach after feeding. Do this for two to three weeks after birth (or, in other words, as you feed it milk or formula), or it simply won’t relieve itself.
Make it past a couple of months, and your eevee should be able to survive on its own, just like any other eevee. But it’s important to remember that until then, it’s a good idea to avoid reintroducing this one to its mother. You may be able to expose it to its brothers and sisters, but the mother may attack your shiny eevee on sight. It’s a leftover instinct from the wild—behavior designed to discourage a shiny from coming back and putting the rest of the litter in danger by drawing in a predator, basically. After the eevee can survive on its own and begins mastering its attacks, the mother may take an ambivalent stance towards her puppy, but it’s unlikely that she’ll ever see it as hers. It’s up to you to give that hatchling the love and affection it needs to grow.
Best of luck, anonymous.