The problem that The Retrievals deals with is epidurals failing during cesarians, which, they're quick to emphasize, is painful, open abdominal surgery. The not-so-simple solution is to convert to general anesthesia (anesthetic gas, IV propofol, etc). This isn't without its risks to the mother and the child, so there's reluctance on the part of anesthesiologists to go that route if there's other options. The result is unnecessary birth trauma.
anesthesiologist here, I really fear a dodgy epidural being used for caesarean section surgical anaesthesia, and if there is any hint that an epidural isnt perfect I pull it out and do a spinal anaesthetic (as long as I have time eg. If the baby can wait long enough). Its a big call which needs to be made quickly. I have a theory that modern epidural medication mix has been dropped to be so low concentration of active drug that it is harder to differentiate a good epidural from a patchy one, and as a result people are topping up patchy epidurals and then running into problems with pain during surgery.
The "risk to mother and child" is referring to using general anesthesia. The "unnecessary birth trauma" is referring to C-section without any anesthesia.