He's fighting these women. They want him out, so he'll stay in.
What remains puzzling to me, is why isn't anyone -- Cain's campaign, media, whoever -- vetting White's story?? A 13-year affair would leave a huge paper trail of evidence. Huuuuge.
Phone records (and only recent ones at that) won't cut it. You could barely innuendo O'Reilly-type shenangigans with that, and she'd still need recordings to back it up.
No, put this woman on the spot, fisk her thoroughly, and vet her story.