Poor Batman. It's no wonder that the Dark Knight is so gloomy - he's just no good at relationships.
First, it was Julie Madison who broke it off with him after his father died at the hands of Sal "The Boss" Maroni (who threw acid at Harvey Dent, turning him into Two Face).
Next was Silver St. Cloud, who discovered Bruce Wayne's secret and dumped him because she didn't want to live with the constant fear of losing him (she later reconnected with Batman after her fiance was killed by the Joker, but in a twist of fate, she was herself killed by yet another one of Batman's enemies).
Then, there was Rachel Caspian, the woman for whom Batman was willing to end his crimefighting career to marry. But she turned out to be the daughter of the murderous Reaper, and as penance for her father's crime, she became a nun.
Oh, and who can forget Sasha Bordeaux, who helped Batman fight crime but was framed and put in jail for a murder she did not commit. There, she was injured by other prisoners and was turned into a cyborg by a secret governmental spy agency.
The list goes on and on, as explained over at DC Comics Database, and as you can see, being Batman's girlfriend is often dangerous to a woman's health. So, if the Caped Crusader asked you to be part of his Dynamic Duo, the right answer is to run away as fast as you could.