I've been unsuccessfully trying to grow herbs (from Trader Joe's) in my apartment -- the plants are relatively and low risk, but I've been struggling to keep them healthy.

After an initial round of heavy harvesting, my parsley leaves started coming in with white waxy spots. It looks like it may be some kind of mildew -- but growth hasn't stunted in the way that mildew usually causes.

This plant is kept in a window with southern exposure, in Brooklyn -- not too cold, not too warm. Any idea what's wrong? How I might fix it? Should I try to salvage the plant or cut my losses?