What happens if the initial treatment for biliary atresia fails?

Liver transplant: If you mean surgery, i.e. Kasai procedure, as "the initial treatment", then liver transplantation is often needed. Untreated, chronic bile buildup leads to cirrhosis and liver failure.

Transplant: Treatment for biliary atresia is a kasai procedure which should be done before 60 days of life to be effective. One third of patients will do well and be cured. One third will do well for a period of time(years) but will eventually need a liver transplant. The final third will fail kasai and need a liver transplant sooner.