Relaxin functions to loosen ligaments which in turn allows the pelvis to spread every so slightly to allow passage of the newborn. I do not know how long the hormone is produced after birth or the half-life of the hormone in the body.
There never has been a report to my knowledge that implicates relaxin with disc herniation.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.