A few restaurants are closed for weeks at a time and some stores have shorter hours but the beaches are empty as they get.
Also, it is hurricane season. Just so you know.

I was just in the islands this past Sept and it was great for me. I'm not into all the crowds so my trip over to STJ was perfect. Spent a few hours at Cinnamon Bay and for about an hour of that time my wife and I were the only ones there, and the other couple of hours there were only two other couples there.

Like Chris said, there were a few closed shops and restaurants, but there was still plenty of others that were open. While I was getting money from an ATM near the end of the afternoon I overheard a few people getting ready to party at a couple of the nightspots. Unfortunately my wife was beat from the heat so we decided to head back to STT to our hotel instead of hitting the party places on STJ.

Hurricane Isabel was in the area while I was there, but she turned north and the only part of it I saw was while flying back to the states. It's still very hot in Sept but the nights cool down to the upper 70s or lower 80s. 🙂

September can be a great time to be in the islands. Lodging costs drop, it's much less crowded, less waiting. But it is hurricane season. Now hurricane season is not a bad thing unless a storm is hammering the particular island where you are, or is just generally screwing up flights. Of course the odds are greatly against that happening. But then again, if you wanted to be in a hurricane, September would be a prime time to choose to go.
It's a risk we choose not to take and we stay out of the Caribbean in August and September. If you do plan to go, you may want to invest in some good travel insurance so that you could cancel if September weather is ugly.