Ratzinger was actually the first person in the Vatican to take the child abuse scandal seriously. He requested the job of investigating it. For example, he went directly against JPII's personal feelings regarding Father Marciel Maciel of the Legions of Christ. Everybody - including JPII - thought this guy was a saint and he was actually a sociopath who did unspeakable things and basically ran an abusive cult. He defied everyone in the hierarchy and exposed the guy.
He requested the task of dealing with the scandal, read every single word of every report, and took it seriously when others wanted to keep their heads in the sand. (Something it seems everyone does in every organization, from the BBC to the Boy Scouts of America.)
I don't think he'd quit over a scandal. I think he's used to that and would be willing to take whatever lumps he has coming. I think it's poor health. He may know something - dementia, cancer, brain tumour, something like that - that means he's not going to be able to do the job any longer.
JPII did a beautiful thing with his life and death. He lived a beautiful witness to the dignity of all human life and showed what a true "happy death" looks like: it's not pretty, it's not painless, but it has its own inherent dignity because it embraces the suffering of Christ. That was JPII's calling. His cross and his charism. But it may not be what Benedict is called to do.