Are students still in Head Start/comparable program or are they on their own?
They're on their own once they get into their public schools.
This "fade" in performance is argued against heavily by Head Start supporters, who try to blame the poor schools the kids are sent to for the problem.
That being said, there is at least one study that looked at various factors including race.
The results showed that the disadvantaged white kids in the program, who tended to be the worst off of all groups, showed the larger and more long-lasting improvements to their performance than black kids.
I'd have to look closer at the study to see if they had and reasoning for why that may be. The "involved parents" argument is probably in play for that, though.