Answer: I have had similar experiences with forget me nots. The good thing is that the plants readily self-sow. With that in mind, I wait until they set seeds, then pull the plants up. The seeds germinate in a short time and healthy new plants will grow where the old, spent ones once were. If you think of forget me nots as short, early season annuals and pull them up when they finish flowering, you won't have to deal with the powdery mildew and mold that they develop when they've finished flowering.
Best wishes with your garden!
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