According to the Wikipedia article on Burnside:
"Burnside was relieved of command on August 14 and sent on leave by Grant; Meade never recalled him to duty. A court of inquiry later placed the blame for the Crater fiasco on Burnside and his subordinates. In December, Burnside met with President Lincoln and General Grant about his future. He was contemplating resignation, but Lincoln and Grant requested that he remain in the Army. At the end of the interview, Burnside wrote, "I was not informed of any duty upon which I am to be placed." He finally resigned his commission on April 15, 1865."
Can anyone hear think of an alternate situation fron OTL that could have occured near the end of the ACW that would have encouraged Burnsides superiors to recommision him, or perhaps have the court which charged him make a different verdict? From what I understand so far he was a good military leader who got a bad reputation from one battle that went terribly wrong due to not fault that was his own.