At least, it did right up until the point that she decided to quit and become a politician. In the end Barbara Gordon ended up retiring a few times from the Batgirl job, the most important being the special solo book (a one-off issue, which is important) where she announced her intention to walk away from crime fighting. Which was done to set up The Killing Joke. Before that, though, Babs had given up on her vigilante lifestyle to continue her public service in a very different sphere. Having revealed her secret identity to her dad who had already figured it out because, duh, he's a cop she officially decided to hang up the cape in 1972's Detective Comics #424. But Batgirl's Last Case, as that story was called, heralded a new chapter in Barbara Gordon's life. She moved to Washington DC and became a member of the United States House Of Representatives. Eventually she gave up on the Congress job after a blind date with Clark Kent gave way to a Superman/Batgirl team up.
Tom Baker is the Comics Editor at WhatCulture! He's heard all the Doctor Who jokes, but not many about Randall and Hopkirk. He also blogs at http://communibearsilostate.wordpress.com/