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Parkerman - What is your phosphate level in the pool?
If you don't know, take a sample down to your local pool supply store as they usually will test the sample for free. If your phosphate level is high, you will have to remove it with a 2 part treatment that draws the phosphate out into a precipitate which the filter then filters out of the water.
You will then need to disassemble your DE filter, as backwashing your filter is not sufficient, by removing the filter elements, removing all of the DE from the elements, then cleaning everything with a diluted solution of muriatic acid. Replace any damaged or torn elements. Reassemble all elements by placing a small amount of silicon on the plastic portion of the filter elements where they attach to the manifold. This will prevent them from becoming frozen together and make disassembly easy the next time they have to be removed.
Test the water again to ensure that phosphate levels are near zero.
Phosphates are food for algae and no matter how much algaecide (Polyquat) you put in the pool, you will not be able to stop or control the algae. Phosphates are commonly found in anti-staining chemicals/treatments as well as organic material (leaves, sweat, grass) that ends up in the water.
And yes, regular brushing does aid in preventing algae from taking hold on surfaces, but if your pool chemistry is not right (Phosphates included) no amount of brushing will prevent it.
This should resolve your problem.