One disease that has become a serious problem in Texas lately on St. Augustine lawns is called Take All patch. It forms large dead patches such as you describe. It's a new disease, only emerging in the last 10 years, and control measures are still being worked out by the experts. Lawn fungicides seem to work. Spreading organic matter (manure, peat moss, corn meal) across the surface of a lawn is the currently favored organic control for lawn diseases, so that could be another option to try.
Meanwhile, take a sample into a reputable garden center and see if they agree that this is what it is. Grubs and chinch bugs can also cause large dead patches to appear. You should see the actual bugs if this is what the problem is. Grubs can be found just underneath the dead grass, which should pull up easily due to all the eaten roots. chinch bugs are small, but you should be able to see lots of them if they're numerous enough to do this much damage. It the problem is insects, there are easy remedies that the garden center can provide you with.