One of the reasons for closing in September is that many employees have family homes that are off-island, and they wish to return to them for the duration of the September Celebrations. It works well for establishments to give employees their paid vacations at a time when they can enjoy them, and at a time when the rate of visitor arrivals is at a natural low point in the year.
Further as Elbert points out so well in his graph, the risk of storms is high and again people like to be "home" when weather threatens. For those owners and workers who are still in the area during September, it's a good time to do annual cleaning, repairs etc all at one time.
This is a seasonal business, no doubt about it.