They're afraid of losing the small percentage of women he retains.
All it will take is one reporter to bring it up with the cameras rolling and the Governor will either:
Get up and leave; torpedo in the side of his bid
Bobble up an answer that doesn't say anything; given his utter failure at such things in the past...another torpedo
Answer the question forcibly and surprise everyone. I don't think he has it in himself to take a stand because it will contradict his previous stances.
Boy, I hope some reporter musters the cajones to do that. Its not like they'll be wanting to interview him after he loses anyway...no risk situation for the reporter.