There is rarely any coach who can teach both beginners and masters well. You do not have a coach for life, no matter how good s/he is. When your child's skill improves, you will have to move up. This is like changing teachers when your child moves from elementary school to middle school, to high school, then to college.
Another reason for changing coaches is effectiveness. Most coaches will become too nice to their long term students, sometimes they may treat them like their own children. It would be hard to put higher demand and discipline on their students if this happens. Changing to a new coach may help put business back on track.
Third reason is playing style. Different coaches have different playing styles, so they teach different strategies. Your child may need to find a style s/he likes.