I’m from the south (in general—I grew up all over it) and I think that anywhere you get a strong accent, there is a tendency towards “axing”. I know in the New Orleans area, like Darwin said, many people “ax” (including the Cajun-French—think of the typical French accent and then say “ask” in it). To be honest, I’ve noticed it all across the south (North Carolina, Virginia, Louisiana, Alabama) and all across ethnic groups (black, white, cajun, you name it). I’ve also heard “ax” coming from a Boston accent.
So I think that’s just what “ask” sounds like when it encounters a strong accent.
And yes, I’ve “axed” a question. My mother just about threw a fit. She’s big on properly pronouncing things and thought it was verbally lazy.
I think she also didn’t want me to develop a strong southern accent. I’ve never really had one.