In determining when a woman is viewed as beginning the birthing process, the Gemara on today’s daf presents the view of the Amora Shmuel who teaches that a woman can conceive and bear only on the two hundred and seventy-first day (a full nine months of thirty days each, plus one day after intercourse) or on the two hundred and seventy-second day or on the two hundred and seventy-third day (conception being sometimes delayed one or two days).
The Gemara identifies this position with a tradition of the Hasidim ha-Rishonim – “the pious men of old” – who engaged in marital relations only from Wednesday until the end of the week in order to avoid the possibility of Sabbath desecration because of the childbirth. 271, 272 and 273 days make up 38 weeks and 5, 6 and 7 days respectively, so that a conception on a Wednesday results in a birth on a Sunday, Monday or Tuesday.
The Ran suggests that ideally the Hasidim ha-Rishonim engaged in marital relations on Wednesdays because a birth on a Sunday, Monday or Tuesday covers the three day period when Sabbath desecration is permitted on behalf of the mother after she gives birth.
The question of whether or not performing activities on behalf of a sick person that are ordinarily forbidden on is considered to be Sabbath desecration that is permitted is raised in a number of places in the Talmud. The two possibilities are whether we view such activities as hutrah – entirely permitted – or dehuyah – that the prohibition is “pushed aside.” It appears that the position of the Hasidim ha-Rishonim was that activities on behalf of a sick person are only dehuyah with regard to, so they did everything they could to avoid such situations.