Grass planted above a septic tank usually has a shallower root structure than grass grown elsewhere on the property. During periods of intense heat and drought, this grass with shallow root structure is more likely to die out from thirst. Grass roots normally reach deep down into the soil so they can capture moisture even during the height of a hot summer. If there's a septic tank or other component of the septic system blocking the roots, they are more likely to turn brown.
Brown or dead grass above the septic system can also be a sign of a much more serious problem: hydraulic failure. This means that the tank is failing to purify the toxic wastewater, which is seeping into the soil and causing your grass to turn brown. Hydraulic failure is typically accompanied by a foul sewage odor, which is likely to appear before you even notice the brown grass. If you're away from your home for a long period, however, you may return to find a large portion of your lawn is brown, an indication that your tank has failed.
If you suspect hydraulic failure, call a professionally licensed septic contractor to take a look at the septic system. If you have an old tank, chances are you will need to replace it, and the septic contractor can give you an estimate on that. If a septic tank contractor is not available, call a professional plumber who'll also be able to give you an estimate.
If your tank is working properly and the brown grass is simply a symptom of hot, dry weather, make sure to water the grass above the septic system especially well. You may want to set up a sprinkler in that area of the lawn to water it regularly. To avoid septic system failures, which can also cause brown grass, have your tank tested and serviced regularly.