In Hitman, can you not play elusive targets that are missed?

Just got Hitman and wanted to play the mission where you have to kill Gary Busey but it says that I missed the mission. I know these missions are timed but does that mean you can't play them anymore at all? If so, then what the fuck is this bullshit? What's the point of timed missions like where people who got the game late can't play them anymore.