If you aren't doing this already, when you clean up the poop in the basement, make certain that you clean it well with an enzyme cleaner, otherwise the scent will still be there. Also it may help (before using the enzyme cleaner) to bring a poop that was already done in the basement out in an area of the yard that offers privacy. The poop from the basement will have odors from the basement that she is already familiar with.
I'm just kind of thinking outside the box and a bit from her perspective with the knowledge of how powerful their sense of smell is and the reactions that are caused (illicited) when their nose is at work. It may help her feel more at ease to go outside.
"If you can't see his soul when you look in his eyes, then you need a seeing-eye dog"