Find out what the charter companies policy is for named storms in the area. They are so hungry for business now that they may refund your charter fee or give you bonus days or another charter should your trip be inerrupted. Also check your credit card. Some prestige cards include trip insurance that may repay you if a hurricaine interrups your charter
Aside from the potential danger and the low rates... a lot of stuff is closed and things are pretty burned out from the summer sun. That said...the anchorages are much less crowded, the water is still beautiful and the weather is fine as long as nothing tropical is brewing.
Check into trip insurance if you go AND if anything is brewing...get back to base and get off the boat!
The previous advice is very good.
Hurricane season is our favorite time of year to sail for precisely the reasons mentioned---fewer boats in anchorages, generally lighter winds and flatter seas. I do know that some charter companies are offering free trip insurance for summer charters. Please compare prices and options, there are many discounts available.
If you choose to go, pay very close attention to the weather and enjoy yourself.
While a large number of places close in the Aug/ Sept/ Oct time frame, most are only closed a single month and they do vary. Few of the major destinations close. Cooper Island typically shut down for a month in that time frame to do maintenance and allow the staff time off. Restaurants also do the same.
I don't know of any marinas, mooring fields or anchorages that close but some of the mooring fields will be undergoing inspections and repairs but this only last a few days at a time normally then they are back in business.
By all means DO Keep a Weather Eye, ZBVI a local AM radio source for weather reports. You will be able to get the NOAA forecast on VHF most locations and just figure the St. John reports and forecast are good for most of the BVI. Lots of locations have WIFI and have your fav weather sights in your computer such as...