I know I can copy a gradient (minus direction) from one object to another, but how do I preserve the direction of the gradient? (I'm using Illustrator CS6)
Drag the Gradient Filled object to the Graphic Styles Panel.
The angle will be retained in a Graphic Style (along with any other appearance settings)
Then, when you need to reapply the gradient, select the new object and click the Graphic Style in the Panel.