The first 48
yes very true, for all crimes, the more time passes the farther the criminal can put himself away form the crime. Not just distance, they have time to change their looks, people forget(we won't for Mike), new murders or other crimes attract attention and get priority.
think about it like this, imagine some pool player we all know got shot and killed in Boston the day before the bombing , ALL Boston's resources were focused on the bombing. I bet that every murder that happened 3 days leading up to the bombing grows cold in Boston. The cops were pulled from one job to the other, That would be a interesting static to follow up on. the exception might be if the person turned himself in or murder/suicide.
it just hurts lots more when its close to home, i really feel for anyone who's direct family gets murdered. If that happened to me, i'd stop everything and search until I found the rat bastard. There would be no stopping me, i wouldnt rely on Law Enforcement alone.