Why did they stop?
May not have worked as well as as they wanted.
> Why did they stop?
Because Kennedy and Johnson wanted manned spaceflight to be reserved for NASA, for propoganda reasons. The Dyna-Soar prototype was 80% complete when the program was cancelled.
"Blackstar" is almost certainly fiction. There's no reason to believe the US has this type of capability -- yet -- but it should have.