Robbery is a serious violent crime (Fox News video is available here). For police not to respond to reports of robberies will only lead to one prediction: there will be an increase in robberies. In a city that makes it extremely difficult for people to use guns defensively, not having the police respond is dangerous.
There is also the James Q. Wilson notion of "broken windows." As the city disintegrates, it may encourage other more serious crime to occur.
Note how different the response to crime here is compared to the sheriff in nearby Milwaukee after their budget cuts. That sheriff cut this public service ad:
"I am Sheriff David Clarke, and I want to talk to you about something personal, your safety. It is not longer a spectator sport. I need you in the game. But are you ready? With officers laid off and furloughed, simply calling 911 and waiting is no longer your best option. You can beg for mercy from a violent criminal, hide under the bed, or you can fight back. But are you prepared? Consider taking a certified safety course in handling a firearm so you can defend yourself until we get there. You have a duty to protect yourself and your family. We are partners now. Can I count on you now?"