I guess I don't understand what you mean by "give him up". I understand he wasn't saying anything. But it's not law enforcement's job to say "gee, he's not saying anything, nothing we can do here!"
With all the circumstantial evidence pointing towards him I can't believe they couldn't find some charge to bring him in on. Not for the murder, but something. This is really common in investigations like this. You obviously can't be the murder charge until you know she's dead, but usually you can find some lesser charge to at least get them in. At a minimum I can't believe they weren't at least keeping track of his whereabouts.