I find that booleans in Maya grow more unreliable as your model gets more complex; as your list of operations on any given surface grows, even if you delete your construction history and model very carefully, what you describe happens more and more frequently.
That said, I don't like the way that screwdriver is modeled. I think it is better to model one section of the piece, create a simple boolean using quadrangular geometry, insert edge loops where necessary to "protect" your edges, then duplicate that piece radially.
I'm attaching a simple tutorial on the process for you - this tutorial is for modeling a fluted column, but the shapes can easily be adapted to make the screwdriver in the tutorial you are following.
creating_a_fluted_column_in_maya_1.pdf