Final answer:
The pudendal nerve is most likely to be injured during a sacrospinous ligament fixation for apical vaginal repair due to its anatomical course near the sacrospinous and sacrotuberous ligaments.
Step-by-step explanation:
The nerve most likely to be injured during a sacrospinous ligament fixation for apical vaginal repair is the pudendal nerve. This is because the sacrospinous ligament fixation involves surgical manipulation near the sacrospinous and sacrotuberous ligaments which contribute to the formation of the greater and lesser sciatic foramina. These foramina allow passage of the pudendal nerve, hence the proximity poses a risk to the nerve during the procedure. Injury to the sciatic nerve is less likely as it is larger, positioned farther away from the sacrospinous ligament, and is not as vulnerable in this surgical approach. The femoral nerve is anteriorly located and not generally at risk during pelvic surgeries, and while the obturator nerve passes through the obturator foramen, it is not in as proximity to the surgical field as the pudendal nerve during sacrospinous fixation.