Well, thats one of the more curious mutatings of many legal systems in the world: Once a case goes beyond a certain stage, its virtually unstoppable at times as a lot of egos, legal and political careers etc. start getting connected to it.
When I read about cases like this Willingham thing, it strikes me as exactly that kind of thing: Some people with a lot to lose realized one day they had backed and persecuted a case that at the last minute turned into a hoax. However, they dont actually care for the guy, and they see ways to still get a conviction and sentence, so in the interest of their careers and to save face, they ll just let it go on.
Its not about justice at that point.
Its amazing how persistent some states/counties insist on not admitting to a mistake in some cases. Willingham is just one, but there are quite a few (not all death row mind you) where its glaringly obvious a major mistake has been made, or where very conclusive evidence is showing up later on basically proving easily it didnt go that way... but for some reason its "too late" then, and technicalities or whatever else is needed is employed to keep the sentence n place.
Some of these last words, though, kinda give you the impression the guy doesnt care one bit for what he has done.