Black spot algae returns because you're not fixing the chemicals.
You can’t scrub black spot algae away — you have to address the underlying nutrient imbalance that lets it come back.
Black spot algae (actually a cyanobacteria) builds a tough waxy layer that shrugs off normal chlorine and brushing. Scrubbing just clears the top; the roots stay in the concrete pores. What keeps it coming back is phosphates — basically algae food. Most pool problems trace back to phosphates.
Test your phosphate level. If it’s above 100 ppb, use a phosphate remover (they’re not that expensive). Then shock the pool hard with liquid chlorine — aim for 15–20 ppm and keep it there for 24 hours. Also check your pH; keep it between 7.2 and 7.4 so the chlorine actually works. Run your pump longer, especially during hot weather.
Once you’ve killed it, brush the concrete weekly anyway. Those roots need to be physically disrupted. If you do all that and it still returns, you might have a circulation dead spot — consider a return jet adjustment or a robot cleaner that scrubs walls.
Your pool doesn’t want black spot algae — it just has the conditions for it.