Continuity mistake: Towards the end when Bruce takes the cat, the wounds on his left cheek change from faded to fresh.
Continuity mistake: In the opening, Penguin's parents look at the cage holding him. From the outside, his shaking is making the cage move slightly side to side. From inside, his shaking is not moving the cage at all.
Answer: Nothing was stopping them. After Penguin's true nature was revealed, they most likely started searching the entire sewer system but couldn't find where his lair actually was so they had no choice but to give up.