Shallowing is created by not coming over the top of the swing path. Usually, your shaft stays under this plane and then moves into a better impact position from there. This usually is created by maintaining width and turning with your body rather than a pulling down motion. Shallowing problems are also derived from a an early release and/or cast of the club during transition, and causes the "STEEP" attack at the ball.
The key to a shallow golf swing plane begins with a full shoulder turn away from the ball. From there, your body, NOT your arms, are responsible for getting the club into the slot. A full turn - with proper body rotation - will provide a permanent solution to Shallowing the club properly.
For a lasting solution to shallowing the club, use this drill to work on emulating a proper body motion that will promote a rotation rather than pull down. Starting the backswing with a very vertical takeaway. This overexaggeration of vertical will make shallowing easier. When this drill is executed properly, the feeling of shallowing the club will become more ingrained and start to feel nature.