The Governors Club is actually thriving and did an excellent job of powering through the recession. As preciously mentioned in another comment, Governors Way is the longest street in the neighborhood with over 100 residences on it. Additionally, the neighborhood has over 400 home sites total, FYI.
The monthly fees are only $250 and it is the only neighborhood that offers 24 hour guard gated security in Brentwood. It also has an Arnold Palmer golf course (fees are additional), tennis courts, 24 hour fitness center, huge pool, kids pool, picnic area to reserve with grills, a park, and some of the most beautiful scenery in TN.
The fees are kept low because the property owner's association owns the original mansion that is in the center of the neighborhood and is used as a revenue generator for private events. Also, every lot owner pays $250 / month to the association so the residents don't have to wait for the community to get built out before appropriate money is into the association.
I hope this helps. I could go on with much more information about the clubhouse, complimentary daycare, restaurants, bars, etc... @ the club, but will deliver that info if you need it.
I am a member of the club and have sold over $25MM in real estate in The Governors Club in the past 2 years or so. If you have any questions, I have or can get you the answers.
Best of luck in your search!