Final answer:
In cases of acute diverticulitis that has failed antibiotic treatment and symptoms persist, surgical intervention may be necessary to remove the infected tissue.
Step-by-step explanation:
The next step for a case of acute diverticulitis that has failed antibiotic treatment and symptoms persist would be to consider surgical intervention. Surgical removal of the infected tissue may be necessary if the infection continues to progress rapidly or if complications such as abscess formation or perforation of the colon occur. It is important to consult a healthcare professional for an accurate diagnosis and appropriate management.