IIRC, the speculation was that he backed out because Byron White was not comfortable with using Casey as the vehicle to overturn Roe v. Wade.
I believe that Kennedy WILL vote with Thomas, Scalia, Roberts and Alito if there is a case that can reasonably be structured to overturn Roe.
I'm not that confident Kennedy would go that far - however, he is more inclined to allow more restrictions on the procedure.
White dissented and joined the opinion stating Roe should be overturned. Amazingly, Roe only survived on a 5-4 vote in 1992.