Gemara

64a (Mishnah): If a man married a woman and she did not give birth in 10 years, he may not neglect Peru u'Rvu. If he divorced her, she may marry another man, and the latter man may keep her for 10 years without children.

If she miscarried, we count 10 years from the miscarriage.

64b - Inference: The Mishnah permits her to marry a second man, but not a third. Our Mishnah is like Rebbi:

(Beraisa #1 - Rebbi): If a woman circumcised two of her sons and they died, she should not circumcise her third son;

R. Shimon ben Gamliel says, she circumcises the third, but not a fourth.

Rava: Regarding marriage, the Stam Mishnah (and the Halachah) is like Rebbi.

65b (R. Ami) If he says that she miscarried within 10 years and she denies it (and asks to be divorced now), she is believed. Had she miscarried, she would not falsely establish herself to be barren.

If she miscarried three times she is established to miscarry (and he must divorce her).

(R. Yitzchak ben Elazar): A case occurred in which he said that she miscarried twice and she said that she miscarried three times. Rabanan believed her. She would not falsely establish herself to be one who miscarries.

Rishonim

Rif: When we believe a woman that she did not miscarry in 10 years or that she miscarried three times, he pays a Kesuvah, for perhaps he did not merit to have children through her.

Rambam (Hilchos Ishus 15:12): If a woman miscarried three times she is Muchzekes to miscarry. Perhaps he did not merit to have children from her. He divorces her and pays a Kesuvah.

Rambam (13): If he says that she miscarried within 10 years and she says that she did not, she is believed. She would not (falsely) establish herself to be barren. If he says that she miscarried twice and she says that she miscarried three times, she is believed. She would not (falsely) establish herself to miscarry. He divorces her and pays a Kesuvah. In these cases he makes her swear Shevu'as Heses that she did not miscarry, or that she miscarried three times, for this claim obligates him to pay the Kesuvah.

Rebuttal (Ra'avad): I see no need for this oath. Chachamim believed her because she does not establish herself to be barren. Also, the divorce obligates him to pay a Kesuvah.

Kesef Mishneh: The husband claims that he is not yet obligated to divorce her. She is like a lender who says that the loan is due and the borrower says that they fixed a later date; the lender swears and collects.

Rosh (6:19): According to Rebbi, a woman who miscarried twice may not marry a man without children. She receives a Kesuvah from her first husband. She is like one who was childless after 10 years with each of two different men. Rashi and the Rif disagree. They say that once she miscarries twice her husband divorces her and pays a Kesuvah. He does not wait for 10 years; perhaps he did not merit to have children through her. She may remarry; we attribute the punishment to her husband. We believe a woman when she says that she miscarried three times, for she would not falsely establish herself to be one who miscarries. Even though she may remarry according to Rashi and the Rif, men are not eager to marry her. My opinion was reasonable, but I defer to their opinion.

Poskim

Shulchan Aruch (EH 154:10,12): If a man married a woman and she did not have children in 10 years, he must divorce her and pay a Kesuvah or marry a woman who can conceive. If she miscarried, we count (10 years) from the miscarriage. If she miscarried three times she is Muchzekes to miscarry. He divorces her and pays a Kesuvah. She may marry someone else.

Nimukei Yosef (21a DH Omar): Since she married b'Heter and many women miscarry at the beginning of pregnancy, even Rebbi agrees that she is not Muchzekes until three times.

Beis Shmuel (27): R. Shmuel (brought in Rosh 6:15) says that the conclusion of our Sugya is like R. Shimon ben Gamliel. However, the Halachah does not follow R. Shmuel.

Beis Shmuel (28): The Rambam (15:8) says that after 10 years without children she gets a Kesuvah only if she claims that his semen does not shoot out at the time of Bi'ah. If not, Chezkas Mamon exempts him from paying. Likewise, when she miscarried three times we say that he did not merit to have children through her.

Rebuttal (Beis Meir): We know that she is ill (regarding childbearing). Why should we assume that his sin is withholding children?!

Shulchan Aruch (13): If he says that she miscarried within the 10 years so she may remain with him and she says that she did not miscarry, she is believed.

Beis Shmuel (29): The Nimukei Yosef (21a DH Omar) says that this is only when we are not concerned lest she desires another, e.g. if Beis Din forced him to divorce. Why must we say so? After 10 years he must divorce her! Perhaps he holds that even after 10 years we are concerned unless she says that he has not been Yoreh k'Chetz for 10 years. Perhaps she miscarried within 10 years! Therefore, he says that she did not seek to be divorced. Alternatively, since she establishes herself to be sterile there is more concern lest she desires another man.

Beis Shmuel (30): Why isn't he believed, Migo (since) he could say that he knows that he is sterile? According to the Nimukei Yosef, we can say that they agree that she miscarried and argue about how long ago it was. Since she became pregnant, it is a poor claim to say that he is sterile. Rashi says that she says that she never miscarried. Rashi can say that he has no Migo to say 'I am sterile' because a person is reluctant to say this.

Shulchan Aruch (14): If he says that she miscarried once or twice, and she says that she miscarried three times, she is believed.

Shulchan Aruch (15): In all of these cases he makes her swear Heses that she did not miscarry or that she miscarried three times, for her claim obligates him to pay a Kesuvah.