I dunno, B, but that's a damn fine question.
I've never read or heard anything that provides a clue but I have ideas. I suspect one reason blacks stay away from the polls is also tied to why they are least likely (of all ethnic groups) to own their own home -- a greater percentage of Latinos, far newer to the US in comparison to Blacks, own their own homes. Hate to say it... hate to throw this excuse out there... but part of it has to do, I believe, with slavery. And what followed, meaning Jim Crow.
Viewing the US from the squalor and hopelessness of their own lives and country, past (and not so past) generations of Italians, Germans, Chinese, even Mexicans saw the US, as Ronald Reagan described it, as a shining city on a hill. By hook or by crook they got here, with the arrivals sacrificing the first generation to help their offspring get a firm footing. Home ownership (an essential to wealth building ford future generations) and the right to have a say in their government's actions, were paramount to achieving their family's goals.
Compare that introduction to the New World to that of Blacks and Native Americans. Their respective histories relative to the European invasion, I believe, effectively destroyed an important part of who they are and saw (see) themselves as. Not for every Black or Native, of course, but for a good percentage. And the effects linger. They have been effectively disenfranchised and have come to view existence, instead of betterment, a reasonable goal.