Once you accept a job from the bulletin board, it will not disappear until you physically delete it, no matter how far along in the story you go.
Source: Experience. I have at least five treasure missions on queue from before the Shaymin part of the story (I forget what it's called, it's been so long).
EDIT: However, jobs on the notice board change after every "day" of play time. So if you do not accept those missions, they will disappear.