People make mistakes, sometimes really big ones. Owning your mistakes is one path to redemption. Compounding your mistakes is the road to perdition.
GM is a perfect case in point. After failing to notify GM car owners of faulty ignition switches for nearly a decade, which resulted in numerous deaths, GM compounded the problem by sending belated recall notices to the survivors of victims. Its careless follow-through generated more ire, louder congressional hearings and car buyer doubts.
In the newspaper world, there was a standing order for staff to pay special attention to any correction going into print. You would be surprised how often corrections are muffed, enraging people who already were miffed. Correcting a correction is the work of fools.
Nothing undermines an apology more than an apology followed by another faux pas. The second flub tells people your apology wasn't sincere, or at least sincere enough to bother to double-check your words. What you intended as remorse comes across as indifference or insensitivity.