If you do something wrong in a call, or do not respond to something that needs attention, you will score negative rep.
An example might be sending an ambulance to the call for the dog hit by a car. Or telling the woman that calls every 3 minutes because her kitchen is on fire to throw water on the grease fire, etc. (Although, listening to the terrible voice acting when you choose the wrong thing in her case is quite comical)
At the end of the duty, look through all the negative rep calls you might have and make sure none of them are more than -3. If they are, you will have to start from 0 again.
You need 3 of these duties (Which are what the game calls each round, or shift) in a row, without more than a -3.