Because St Aug propagates over the surface of the soil, if you run a dethatcher you will shred all those stolons and kill the entire lawn. If you have a thatch problem, then you are doing something wrong.

Usually thatch forms in St Aug because of too frequent watering and too frequent fertilizing. That kind of care allows the roots to develop so close to the surface that they need not even enter the soil. Thus the entire plant can live above the surface.

For your grass you should be watering once per week during the summer heat and monthly the rest of the year. This summer my grass was suffering badly so I had to water two weeks in a row for 7 hours each time. I watered 5 hours on Tuesday morning (our designated day to water) and 2 hours on Tuesday night. Normally I water 1-3 hours per week to get enough water to last all week. But after 20 months of deep drought, the grass was going downhill. The extended watering perked it up and I've been able to maintain it the rest of the summer with less water.

Also you should be mulch mowing every week at your mower's highest setting. The clippings will decompose and return valuable nutrients to the soil allowing you to fertilize less. By mowing at the highest setting you will be shading the soil better and keeping it cooler. Cooler soil does not lose as much moisture to evaporation. I usually (half jokingly) suggest that St Aug owners weld their mower deck at the highest setting. There is NEVER any reason to lower the deck on St Augustine.

I fertilize with organic fertilizer 5 times per year on the federal holidays. I start on Washington's Birthday and end on Thanksgiving. If you want to use synthetic fertilizer you can follow a similar schedule but skip the 4th of July (too hot) and don't fertilize as early as I do. Wait until you have mowed the grass for the second time to ensure you have active roots to take up the fertilizer. Organic fertilizer works much differently so you do it a little different.

I have St. Augustine that has a lot of thatch as well. If I dethatch on the highest sitting, apply my fertilizer and top dress with sand over the top to keep out the heat will that help the St. Augustine to grow back. I see that it works well on the golf courses.