Green again?

I've done this to myself 4 times in 2 years. Let chlorine get to low again. I normally keep the pool cover on to slow down evaporation, but I was told the draw back sometimes is algae. In the pass I increase the chlorine level off the scale of my tester and ph is in normal range, it bounces back in 3-5 days. This time not. I stopped using tablets 6 months ago and only using chlorine. I was reading here about stabilizer importance and that tablets have stabilizers, helping to control chlorine lose. I added tablets yesterday to get stabilizers going.
Would it be advisable to remove the cover, rater than leave it on and any other advise would be greatly helpful.
Thank you in advance with any pointers, Jim