Why did this series fail?
I have some thoughts on this. First, "bad girl" shows seem to be on the decline, much like the "bad girl" comics that faded away years ago. Dark Angel is gone. Buffy is on the decline; no one even wanted the animated series. Xena is gone. These shows all offered sexy female stars who were also bad ass, superhuman, butt kicking action heroes.
But Buffy and Xena, and to a lesser degree, Dark Angel, had much stronger, more evocative settings. New Gotham didn't have a great deal of atmosphere. Buffy, Xena, and Dark Angel all offered a great degree of originality. They were very distinct from one another, despite many superficial similarities.
Birds of Prey had the potential for this, but for some reason it just didn't happen. One of the strengths of the comic is a strong and interesting relationship between Oracle and Black Canary. This didn't seem to get translated well into the show; maybe the actresses didn't click, or maybe it just wasn't in the scripts.
The show had high production values, and a comparatively big budget for special effects. But you know, it seemed wasted. Take a show like Star Trek, throw in money for special effects, and that helped promote the story, bringing the setting to life. The show probably would have been more successful without wasting all that money.
The action scenes weren't terribly interesting. That's really not good, for an action show. Buffy and Xena both succeeded in doing good action, in very different ways; Birds of Prey did not.
Better scheduling may have helped, as noted by some of the posters above. Emphasizing the Batman connection as much as they did probably didn't help them much. They're not Batman, and they aren't even similar to him. If you were watching a segment of the show, and didn't know any of the back story, nothing about it would say "Batman" to you.
It's a shame the show won't be given a chance to be re-tooled. There's potential there. The scary part is they may be replacing it with another super-hero series called "the Black Sash." I don't know anything more about this replacement, but hopefully it will offer something more than all the failed super-hero shows that precede it.