If you get algae, you are not cleaning well enough or often enough. If there is any amount of algae left alive, in a little pockmark or scratch, even, it will re-bloom quickly. This is why plastic is a bad choice. The algae are small enough to be invisibly caught in those little crevices that you create and then worsen every time you scrub.
Don’t use any algicide type products to clean a water dish. You can poison the cat. For now, use a VERY dilute bleach solution with dish soap, try not to rough up the plastic any more than it is by scrubbing hard, and remove all visible traces. Then rinse like crazy. You will be able to get a respite from the problem, but you won’t get rid of it forever. With plastic dishes, you may need to clean them daily, and refill your water reservoir daily.
If you want to be able to not worry do much about the surface problem, switch to metal or ceramic. Those are not immune to algae, but you won’t have as much problem with scoring it up and making places for algae to survive to re-bloom.
Your best bet is to change to a metal or ceramic fountain. Moving water makes a huge difference, and cats also tend to prefer it, and drink better. With those, you’d still need to clean them thoroughly at least monthly, and change a filter monthly.
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