Final answer:
Based on the information provided, the most likely cause of the patient's recurrent second-trimester pregnancy losses is cervical incompetence. This condition leads to premature cervical dilation, often resulting in miscarriages during the second trimester.
Step-by-step explanation:
The most likely etiology of the patient's recurrent pregnancy losses, based on the information provided, is B. Cervical incompetence. This condition refers to a weak or insufficient cervical structure that can result in the premature dilation and effacement of the cervix, often leading to second-trimester miscarriages, which matches the patient's history. While her retroverted uterus is noted, this is typically a benign finding and is not usually associated with recurrent miscarriages. Paternal balanced translocation is less likely since her partner has children from a previous relationship, suggesting no issues with his sperm. Maternal balanced translocation could also be a possibility, but less so than cervical incompetence as it usually leads to first-trimester miscarriages. Amniotic band syndrome is very rare and typically results in distinct physical abnormalities of the fetus, which are not mentioned in the scenario. Hence, the history strongly points towards cervical incompetence as the cause of the recurrent second-trimester pregnancy losses for this patient.