Here's the three basic rules for growing great turf:
1. Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. If your grass looks dry before the month/week is up, water longer next time. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.
2. Mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. Bermuda, centipede, and bent grasses are the most dense when mowed at the lowest setting on your mower. Dense grass shades out weeds and uses less water when tall. Dense grass feeds the deep roots you're developing in 1 above.
3. Fertilize regularly. I fertilize 4 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above.
We're in the time of year where I can't just make a blanket statement that you have a fungal disease (easily treatable). Usually a growing dead spot, especially one that is nearly circular, is a fungal disease. But in the late summer there is a chance you have grub worms eating your grass roots. The organic treatment for fungal disease is to apply ORDINARY corn meal at a rate of 20 pounds per 1,000 square feet. Give that 3 FULL weeks before you decide whether it is working. Corn meal only works if you have not used any chemical antifungal agents (like sulfur, baking soda, or the commercial chemical fungicides). An alternative to corn meal is milk sprayed at 3 ounces per 1,000 square feet. Any kind of milk will do - chocolate, spoiled, powdered, 2%, skim - anything. The idea is to get some really great protein down on the soil.
The organic treatment for grubs is to use beneficial nematodes. These guys bring a disease to the grubs that kills them in 24-48 hours. The disease is harmless to people, pets, birds, reptiles, fish, worms, and most beneficial insects. The soil must be moist for these guys to survive. I like the BN from the following website.
http://www.hydro-gardens.com/guardian_l ... atodes.htm
I can get them locally (San Antonio) for about the same price as online.