Depends on whether you believe Perry's decline was due to heterodoxy on issues or poor debate performances.
I don't think it was due to either per-se, but rather that the media essentially began making fun of him for each. If you look at polls, after 2 terrible debates he was still doing fine. When he started to tank was well after his second terrible debate, when the media really dog-piled on him. It was the negative coverage more than what he actually did that killed him. Just weeks before he was The Jobs Governor, The Straight Shooter, The Conservative Icon. Then he became The Illegal Lover, The Unprepared Newbie, The Mumbling Drunk Uncle.
I think Cain will just go from The Likeable Guy, The Outsider, The Businessman to: The Amateur, The Ignoramus, The Latest Flavor Of The Week.
They actually can't get him on heterodoxy cause he just adopts the most right-wing position on everything as a default. He has never deviated from that because he has never done anything that requires governing, and he never has doubted his positions because he doesn't think hard about anything.