1. There is a dispute about the law in the case of a child who is born circumcised.
2. A Bris Milah may not be performed on Shabbos for a baby born after eight months of gestation.
3. A baby certainly born after only eight months is considered Muktzah.
4. Any baby that lives for thirty days after birth is not considered a Nefel, even if he was born early.
5. Any animal that is eight days old is not a Nefel.
A BIT MORE
1. Tana Kama: Beis Shamai says that some blood must be drawn from the area of the Bris. Beis Hillel says that this is not necessary. Rebbi Shimon ben Elazar: Both Beis Shamai and Beis Hillel agree that blood must be drawn. The argument is whether a convert who is already circumcised requires a Bris.
2. This is because a baby carried for eight months (in the times of the Gemara) was not going to live. In a case where there is merely a doubt about whether the baby will live, the Bris may not be performed on Shabbos. We do not desecrate Shabbos for a Bris when it is unclear that the Bris is necessary (as a Bris is not given to a non-viable, eight-month baby).
3. This is because it is assumed that the baby is not going to live (during the times of the Gemara, if his hair and fingernails have not yet formed -- Tosfos).
4. This is derived from the verse, "And his redemption should be performed from when he is one month old."
5. This is derived from the verse, "And from the eighth day onward it will be accepted as a sacrifice...."