Rabbi Bachrach (Chavat Ya’ir, no. 31) was asked by a certain errant woman who sinned promiscuously, became pregnant and had regrets. Would she be permitted to abort? He cited the above mentioned Talmudic source (Arachin 7a) and permitted her to do so in order to save herself from a life of agony.
The famous Rabbi Ya’akov Emden (She‘ilat Ya’avetz I:43) was asked a similar question by a married woman who sinned promiscuously, and gave her a similar permit to terminate the fetus. However, he concluded his words with the cryptic statement, “Any wise person can understand that lechat‘chila it is prohibited to kill, although Bet Din does not administer capital punishment for killing fetuses”.
Rabbi Moshe Feinstein (Iggerot Moshe, Choshen Mishpat II:69 par. 2) claims that, with the above statement, Rabbi Emden recanted from the permit. But Rabbi Eliezer Waldenberg (Tzitz Eliezer IX:512 part 3) understood his words as teaching that if not for grave circumstances, one should not easily permit abortions for just any minor reason (such as financial distress of a woman seeking career advancement etc.).