When a root canal fails it is usually do to one of the following:

Unusual and undetectable tooth anatomy.
Small accessory and lateral nerve canals that can not be instrumented.
Cyst formation
Cracked tooth

Most of the "failures" can be saved, with the exception of a severely cracked tooth,  with a surgical procedure called an apicoectomy. This surgery involves removal of the the root tip or "apex" of the tooth root. This is normally where abnormal root anatomy and extra canals are present. During the procedure, the area around the root tip is also cleaned or curettaged to remove any granulation (abnormal healing) tissue and cystic formations. Apicoectomy is an in office procedure performed by an Oral Surgeon. The area is numbed with a local anesthetic to relax you. Pain medication will be prescribed to keep you from experiencing any discomfort. The area may be sore for three to four days days.

Surgical Details

The gum is reflected (lifted) from an area adjacent to the root area of the tooth. Access to the root tip is then made by removing the thin bone covering the end of the root. A small part of the the root tip is then removed and the remaining root is checked to make sure it is sealed. Apical or Retrofilling (reverse filling)  will be required to seal all canals that are found that are not properly sealed . Without proper sealing of all the canals present  in a tooth the procedure will not be successful.

The area around the root tip is then cleaned and curetted. The gum is placed back into position and sutured (stitched). After healing all infection at the tip of the root should disappear and bone should heal to fill in the area around the root tip.