The decision to not act in a criminal justice matter could involve the desire of the law enforcement agency involved to collect additional information on a suspect or group of suspects without tipping the suspect(s) off that it is being investigated. The desire on the part of police or the prosecutor's office to see where an investigation will lead before making arrests is usually predicated upon the belief that there is a hierarchy involved in the criminal organization and that the decisionmakers at the top of that organization can be indicted if the investigation is allowed to run its course.
More often, and possibly more relevant to the question, is the decision by prosecutors not go forward with a trial even though they are confident of the guilt of the suspect. This occurs when the police and prosecutors believe they have identified the guilty party, but do not believe they have sufficient evidence to convict that party in a trial. The difference between believing and proving beyond a reasonable doubt can be considerable, and prosecutors frequently have to make judgement calls on such matters, which they recognize could risk allowing a guilty party to continue to commit crimes.
In both of those instances, the decision to not act can be both easy and appropriate. Where the appropriateness of the decision to not act becomes more questionable is when financial considerations are an issue. A major criminal trial that could last for months is both very expensive, and ties up staff and resources for an indeterminate period of time. Decisions are sometimes made to avoid a trial because of these factors, with the hopes that a plea arrangement will occur. Such an arrangement would involve a lesser penalty for the suspect or defendent, but saves time and money for the city, state or county.