My guess is that it's probably cultural. What has the temperatures been like? How much and how often have you watered? Fertilizer? Soil? Pots or in-ground?

Rodney

Temps have been high, as is usual for this time of year. There has been a lot of rain compared to most summers, but if it doesn't rain an appreciable amount for three days, I water.

They are in raised rows with a wood chip mulch. Other years I have grown my parsley in deep raised beds. No fertilizer, soil ok but not great.

Could it be too much moisture causing a fungus?