Gemara

(Beraisa - R. Eliezer): A child may nurse for 24 months. After this, it is like nursing from Sheketz (a disgusting thing);

R. Yehoshua says, he may nurse for four or five years. If he stopped nursing after 24 months and resumes, it is like nursing from Sheketz.

Contradiction (Beraisa) Suggestion: Perhaps human milk is forbidden!

A Kal va'Chomer supports this! We are lenient about touching animals (every living animal is Tahor), but we are stringent about their milk (of Tamei species). We are stringent about touching people (a living Yisrael can become Tamei), all the more so we should be stringent about their milk!

Rejection: "The camel" (it is forbidden in Parashas Shemini, and again in Parashas Re'eh; the repetition forbids its milk) "... it is Tamei", but milk of humans is permitted.

(Rav Sheshes): It is not even a Mitzvah (mid'Rabanan) to refrain from human milk.

Answer: Milk that separated from the breast is permitted. Nursing (above the permitted age) is despicable.

(Beraisa - R. Yehoshua): A child may nurse until four or five...

Contradiction (Beraisa - R. Yehoshua): (He may nurse) even if he can carry a bundle on his shoulder.

Answer: This is the same Shi'ur (four or five, depending on how healthy he is).

(Rav Yosef): The Halachah follows R. Yehoshua.

(Beraisa): If he ceased nursing after 24 months, he may not resume nursing.

Question: How long is considered that he stopped?

Answer (Rav Yehudah bar Chaviva, citing Shmuel or a Beraisa): It is three days.

Rishonim

Rif and Rosh (5:18): The Halachah follows R. Yehoshua, who permits a child to nurse for four or five years. If he stopped nursing after 24 months for three days and resumes, it is like nursing from Sheketz. The Yerushalmi explains that this is if he was healthy when he stopped. If he was sick, he may resume nursing.

Ran (DH Tanu): Mid'Rabanan, nursing (after the permitted age) is like nursing from a Sheketz.

Rambam (Hilchos Ma'achalos Asuros 3:5): A child may nurse for four or five years. If he was weaned and stopped nursing three days or more because he was healthy, not amidst sickness, he may not resume nursing. This is if he was weaned after 24 months. Within this time, even if he was weaned for a month or two, he may resume to nurse until 24 months.

Beis Yosef (YD 81 DH u'Mah she'Chosav Aval): 'He may resume to nurse until 24 months' implies that the Heter to nurse four or five years is only if he never ceased. If he ceased within 24 months, he may not continue after 24 months. This is reasonable, but I do not know from where the Rambam learned.

Lechem Mishneh: Some say that the Rambam means even if he was weaned for a month or two or 10, until the end of 24 months, he may resume nursing until four or five. The Beis Yosef's explanation is better.

Hagahos Maimoniyos (4): If we estimate that the child is dangerously sick, in any case he may nurse.

Rosh (ibid.): The Shi'ur is four is if he is healthy, and five if he is not. The Yerushalmi says that the Shi'ur of stopping is 72 hours. If he was sick, even if he stopped for a long time, he may resume nursing.

Rosh (19): We forbid milk that did not separate, lest one nurse from a Tamei animal.

Ran (Avodah Zarah 7b DH umid'Amrinan): R. Chananel permits to nurse a baby from a Nochris only if no Yisraelis is available. We assume that a baby is in danger if he lacks milk. A Tosefta equates this to suckling from a Tamei animal. Others say that we are concerned lest the Nochris kill the baby. The Rashba says that it is a mere Midas Chasidus to nurse from a Yisraelis, for the nature of Yisraelim, to be merciful and have shame, affects the milk.

Poskim

Shulchan Aruch (YD 81:7): A woman's milk is permitted if it separated, e.g. she milked into a Keli (or hand). If a Gadol nurses from the breast, it is like nursing from a Sheretz (even if she milks into his mouth).

Beis Yosef (DH Chalav): Rashi says that 'separated' means into a Keli. The same applies if it is in the hand. He excludes if the milk is on the breast, or milking into the mouth. These are as if the milk did not separate.

Shach (18): Into the mouth is forbidden even if there is no contact.

Sifsei Da'as (17): The Heter is only for a Choleh. It is permitted even if there is no danger.

Kaf ha'Chayim (50): Because we do not eat human flesh, nursing can be confused with suckling from Sheketz. If the milk separated, it looks like regular milk.

Shulchan Aruch (ibid.): We give lashes for this mid'Rabanan.

Source (Gra 25): The Gemara needed to cite Rav Sheshes, who says that it is not even a Mitzvah (mid'Rabanan) to refrain from human milk, to ask a contradiction. If the Isur to nurse (past the permitted age) was mid'Oraisa, we could have asked directly from the Beraisa that expounds that human milk is permitted!

Shulchan Aruch (ibid.): A child may nurse for four years if he is healthy, or five years if he is sick.

Shach (19): A weak child may nurse until five. He need not be sick.

Shulchan Aruch (ibid.): This is if he did not cease. If after 24 months he was weaned for three full days, i.e. 72 hours, they may not return him.

Pischei Teshuvah (16): Some say that weaning early prepares a child more for Torah. Adnei Paz refutes this. It is forbidden to wean before 24 months, unless pregnancy or another matter forces this.

Shulchan Aruch (ibid.): This is if he was weaned amidst health. If he ceased amidst sickness, because he could not nurse, he may resume. If there is danger we return him even after many days.

Kaf ha'Chayim (56): If the child ceased to nurse because the mother was sick, he may not resume, for this shows that he is healthy (he did not need to nurse from another woman).

Shach (21): If one is sick without danger, it is forbidden. Even though the Isur is mid'Rabanan, we do not permit an Isur mid'Rabanan unless there is danger. We do not distinguish a minor from an adult, for we do not directly feed Isur to minors.

Shach (22): When we return due to danger, it is only for as long as there is danger.

Shulchan Aruch (ibid.): Within 24 months, even if he ceased amidst health for a month or two he may resume to nurse until the end of 24 months.

Gra (30): This is the Rambam's opinion. The other Poskim disagree. (He may resume until four or five.)

Rema: Milk of a Nochris is like milk of a Yisraelis. Nevertheless, one should not nurse a baby from a Nochris if a Yisraelis is available, for a Nochris' milk blunts the heart and breeds bad nature.

Rema: A nursing woman may not eat forbidden food.

Shach (25): This teaches that even if she is in danger and may eat Isur, someone else should be hired to nurse.