What are the health consequences of a heart rate of 45-50 BPM during contractions from nuchal cord?

Most likely none. It is quite common for infants to experience a slow heart rate during contractions when mother is pushing. However, if the infant is experiencing slow heart rate early in the labor process it may indicate that the baby is compromised. Most infants can tolerate this without long term damage for a short period of time, but ongoing heart rate drops need immediate evaluation.