Gemara

12b (Mishnah): If one said 'I will be a Nazir when I have a child', and his wife miscarried, he is not a Nazir;

R. Shimon says, he stipulates. If the baby was viable (but just happened to die), I am a Nazir due to my vow. If he was a Nefel (stillborn), I now accept Nezirus.

Yevamos 35b (Mishnah): If a Yevamah did Chalitzah and was found to be pregnant, if she gave birth to a Nefel, he is forbidden to her relatives, and she is forbidden to his relatives and to Kohanim. If she had done Yibum and gave birth to a Nefel, they may remain married.

R. Yochanan holds that Chalitzah and Yibum of a pregnant woman are valid. He holds that if Eliyahu would tell us that she will miscarry, we would permit her to do Yibum or Chalitzah. Even now (that Eliyahu didn't come, but we see that she miscarried), retroactively the Yibum or Chalitzah was valid.

Nidah 43b (Mishnah): A one-day old exempts his mother from Yibum.

44b - Suggestion: This is unlike R. Shimon ben Gamliel, who says that a baby that died within 30 days is a Safek Nefel!

Rejection: The case is, we know that he had a full term pregnancy. Even R. Shimon is not concerned for a Nefel in this case.

Shabbos 136a: If a baby yawned and died, all assume that he was a Nefel. They argue about a baby who fell from the roof or was eaten by a lion (within 30 days). R. Shimon holds that he was a Safek Nefel. Chachamim hold that he was alive.

Rishonim

Rambam (Hilchos Yibum 1:5): If a man died and then his widow miscarried, she does Yibum (or Chalitzah).

Poskim

Shulchan Aruch (EH 156:4): If a man died and his wife was pregnant, if she miscarried she does Yibum (or Chalitzah).

Source #1 (Beis Yosef DH u'Mah she'Chosav v'Im): R. Yerucham and the Rambam say so. Yevamos 35b says that if Eliyahu would tell us that a pregnant woman will miscarry, she could do Yibum.

Source #2 (Bedek ha'Bayis DH uv'Hedya): The Mishnah explicitly says that if a Yevamah did Yibum and gave birth to a Nefel, they may remain married.

Rema: Some say that even if he was born dead, and even if we are unsure whether or not he had a full term, she does Chalitzah, but not Yibum.

Source (R. Peretz, cited in Tur): R. Shimon holds that if one said 'I will be a Nazir when I have a child', and his wife miscarried, he is a Safek Nazir.

Beis Yosef (DH u'Mah she'Chosav b'Shem and Bedek ha'Bayis DH Tzarich): Presumably, the Halachah does not follow R. Shimon against the majority!: Even though we say that the first Tana is R. Yehudah, the Halachah follows R. Yehudah against R. Shimon. Perhaps they argue only about Safek Nezirus, but all agree that we are stringent about Chalitzah and Yibum.

Rebuttal (of R. Peretz - Beis Yosef): Nevertheless, we do not abandon a Gemara that explicitly discusses Chalitzah and Yibum to learn from Nazir.

Defense (Bach DH u'Mah she'Chosav): Surely, R. Peretz does not argue with the Gemara in Yevamos! Rather, he explains that if she miscarried a Vadai Nefel, she may do Yibum. If it is possible that he was a nine month baby, she may not do Yibum, for we learn from Nazir that he is considered a child. However, Nezirus depends on the way people speak, and Yibum depends on "his (the deceased's) name will not be erased." If the baby was born dead, his father's name was erased! A Mishnah teaches that a one-day old baby exempts his mother from Chalitzah or Yibum. We establish that this is when we know that he was born after nine months. This implies that had he been born dead, he would not exempt her.

Chazon Ish (EH 115:8): It is astounding to call a baby born dead a 'son', even according to how people speak. It is unreasonable to say that he is considered a son before birth. Rather, R. Peretz is concerned lest he died after his head emerged. Emergence of the forehead is birth, but we cannot check for life until his nose or heart emerges. Perhaps when we are unsure whether or not he was born after nine months, all agree with R. Peretz!

Prishah (16): If we know that he was premature, even if he was born alive R. Peretz surely agrees that his mother is not exempt.

Teshuvas Ben Lev (3:44): R. Peretz could mean that whenever we are unsure whether or not he was born after nine months, she does Chalitzah, even if he was born dead. Or, whenever we are unsure about his months or he was born dead, she does Chalitzah, but if we are unsure about his months and he was born dead, she may do Yibum. The wording is difficult according to both explanations.

Question: According to the latter explanation, why didn't R. Peretz learn from Nazir that in all cases she does Chalitzah?

Answer (Ben Lev): Perhaps he holds that if we are unsure about his months and he was born dead, he is not called a child and there is no Safek Nezirus. If so, we require Chalitzah only when he was born dead and we know that he was a nine-month baby, or he was born alive and we are unsure about his months. If he was born dead and we are unsure about his months, she may do Yibum! Tosfos (Nazir 12b DH Hepilah) says that the first Tana says that he is not a Nazir when 'we are unsure about his months, or he died inside his mother.' The case of dying inside his mother must be when we know that his months were complete. If not, even if he was born alive, he is not a Nazir! Also R. Shimon discusses only these cases, but not when he was born dead and we are unsure about his months. All agree that even a baby born alive is considered dead if he yawned and died (Shabbos 136a). However, perhaps this is mid'Oraisa, when we are unsure about his months, but mid'Rabanan it is a Safek.

Question: In Chulin 72a, we decreed Tum'ah lest a baby stuck its head out and the midwife did not know. Here also, all should agree that we are concerned lest its head came out alive!

Answer (Ben Lev): There, there is only one Safek, for even a Nefel is Tamei. Here, even if he was born alive, if he was a Nefel, Yibum is permitted.