Though I think that some cases should not be closed, others definitely should be. When a case has been open for so many years without new evidence, they should close the case. If there is to be new evidence then maybe the police should re-open the case - if there is enough evidence! Saying that, the evidence also needs to be beneficial to the case.
As someone who is unsure about what classifies as good and bad evidence (I do English Literature and Language for reference), I also don't know when cases are shut. I have watched enough police TV shows and documentaries though, like Sophie: A Murder in West Cork.
This documentary showed the emotion from her family - especially her son who was 15 years old at time. Her son still wants to find the killer, and I don't blame him (like the McCann's who want to find their daughter); however, the amount of resources that have been used must be an incredible amount.
At some point these resources could be used on more current cases in order to solve them, potentially, quicker. The likelihood of finding someone after the first 72 hours in more likely than the time afterwards, with 3/4 of missing people being found within the first 24 hours. Surely this statistic proves that some cases after a certain extent of time should be closed.
Again, this should be taken with a pinch of salt as the victims family will obviously want to find the person who committed the crime so the police have to be cautious.