I could go several different ways with this, but I will just focus on the "as soon as a moment presents itself" part. By the end of 2011, Wren had already chased off Clark and many others and pushed Cox into retiring. Much of the damage we keep hearing about was already done and apparently everyone hated him. But he survived the biggest collapse in Atlanta Braves history.
Maybe JS didn't have the ultimate approval from his superiors to fire Wren at that point. JS deserves blame here for sure though.