Keep my cement patio clean after washing it?

Is it in the shady side of your house???

Sound like a mold situation. Get a mold preventer or try a concrete sealer to keep mold and dirt from getting into the pores.

Sounds like mold or mildew. Use a commercial mold remover or try vinegar on it and a good scrubbing. Mildew penetrates the surface and all the little nooks in the cement. You have to remove it completely or it will just regrow. A thorough cleaning should keep it a bay.

Ken is right, clean it really well with a mildewcide for concrete then seal with concrete sealant after it dries

Agree with above. And each time you powerwash the unsealed surface you are making it easier for mold to grow. Once your patio is thoroughly sealed, you may want to sweep with a blower and wash and rinse with your regular hose.