I do not mind being told I am wrong and here are some good reasons for prosecuting the suspect. I do take exception to replies (yes, that means more than one member) like the one below which dismiss the question without the member showing that they have even thought about it.
I think the answer below is about the best answer I can get. After reading this thread I agree with it 100%. I am unlikely to post again in this thread in the short term. I apologize for not realising the question is such a hot-button issue.
If I may put questions back to you?
How long would one need to be crime free after a murder for punishment to be no longer 'valid'? You choose twenty years, but if it was ten or five years would that be good enough?
Should it matter the number or type of murders? Twenty years for an adult? Ten for a child murder? Add five years for sexual assault? Thirty for a police man murdered in the course of his or her duty? What about a racially motivated crime? If the person ran the gas chambers in belsen?
What quality of life during the twenty years? Should a speeding ticket result in prosecution, or would it need to be drunk driving, or a rape? Supposing he was suspected of further crimes but had been more careful and the police had been unable to prove it and the 'cold case' is the chance to put away a serial offender just as tax evasion was the method of arresting Al Capone?
If it was coming up to the twenty year limit when should it be? Arrest before twenty years? Brought to court or convicted. Would it matter if the defence dragged out the case so the twenty year limit was passed and the case had to be dropped.
The problem is this all becomes very arbitrary. I would say the simplest rule is that if the offender is alive and able to plead (i.e. not demented, in a coma), then they should be charged and tried. I can see that there might be an argument that if the victim wished the case not to be pursued after twenty years then this might be grounds for not pursuing the case (remembering that the particular case may merely be the one of a series of crimes and there may be a public interest in pursuing the case regardless of any individuals wish).
I can see an argument for a criminal who makes a confession after e.g. thirty 'blameless' years pleads guilty and fully co-operates, usually receiving a non custodial sentence.
I also agree that in a rational society there might be an agreed limit to how much to spend on investigating a crime. Indeed there might be an argument for having murder insurance which would pay out for the investigation, and investigatory agencies could compete for the murder as it would be income generating.