I hate to say but I suspect it's almost entirely because of poor work by Rodie. It seemed strange to leave so much about the original investigation not touched upon, and the things that were, were things being done now because they weren't done then.
And honestly, focusing on the ex having remarried so quickly - hello, Rodie, with six marriages under your belt. How would his relationship history hold up under close scrutiny? I know the partner made a comment about that, but it was fleeting compared with the amount of talk made about the suspicious-ness of the ex's behavior, based on his marital history. Personally, the ex was also very smart to not talk to the police without legal counsel present at any point. That should be the first thing anyone is ever taught about talking with the police. Do not buy into "if you're innocent, why wouldn't you talk/come in/offer DNA"? There's a million reasons to have a lawyer at your side and not a single good one for cooperating just to prove you are "not suspicious."
I doubt without a confession that they will ever be able to close the case.