I've been experiencing some issues with mine, and from what I gathered if the booster is failing or has failed it would result in a hard pedal and diminished stopping power from a driver standpoint. What you're describing almost sounds as if you may have a small leak. Have you checked for a leak? With the pedal dropping further than normal, I would look there. It could be you need to adjust the rear brakes, if they are out of adjustment that can cause the pedal to drop more than normal. Just a couple of thoughts for you to consider.

Edit: Something for you to try, pump the brakes 3 or 4 times with the car not running, while holding the pedal down start the car, does the pedal drop some and seem to get easier push?