Why Barbiturates are usually not given for pain relief during active labor?

They rapidly transfer across the placenta, and lack of an antagonist make them generally inappropriate during labor.

Barbiturates are rapidly transferred across the placental barrier, and lack of an antagonist makes them generally inappropriate during active labor. Neonatal side effects of barbiturates include central nervous system depression, prolonged drowsiness, delayed establishment of feeding (e.g. due to poor sucking reflex or poor sucking pressure). Tranquilizers are associated with neonatal effects such as hypotonia, hypothermia, generalized drowsiness, and reluctance to feed for the first few days. Narcotic analgesic readily cross the placental barrier, causing depressive effects in the newborn 2 to 3 hours after intramuscular injection. Regional anesthesia is associated with adverse reactions such as maternal hypotension, allergic or toxic reaction, or partial or total respiratory failure.