Framing
Instead of just asking "why" over and over again, soliciting the same non-responsive answer, how about trying a different approach. This is not the hardest question to ask, I don't think. Here's my stab at it:

Ms. Whitman, there are a few qualities that might lead a person to make the mistake of not voting, like apathy, forgetfulness, elitism and laziness. Which one of those would you say describes the reason why you didn't?

Then the followups kind of ask themselves.