Depending on which constitituents in the dispersants, 10-20 days.
"What happens to the crude when they become ineffective?"
By that time, the surfaces of the microscopic oil droplets have been colonized by bacteria which are eating the oil. The bacterial coating acts as a surfactant layer, so the oil stays "in solution", same as with the dispersant.
As the bacterial continue to eat the oil, the oil droplets shrink until the remaining oil is no longer providing sustenance. All that is left is the really high molecular weight stuff (same as is in tar balls), which is much less toxic.
Basically, the end result is a bunch of non-toxic microscopic tar balls that sink to the bottom of the GOM and stay there. By that time, the material is harmless to marine life.
Thanks for your response.