Can you post a screen capture. About the only work planes that are fixed are the Origin Work Planes, all the rest should be able to move. Yes the feature on the work plane should move with it.
You could also try to redefine the plane. You could use a offset plane as new definition I assume.
Just ensure you define the new plane dependent on geometry that has been created prior to the
plane you´re talking about. If you don´t do so you won´t be able to move it up in the browser
hierarchy to redefine your workplane to.