Black Eye Susan's die again
You are probably seeing symptoms of Septoria leaf spot, a fungal disease of Rudbeckia plants. Septoria leaf spot symptoms start as small (1/8 inch) round dark brown spots on lower leaves that may enlarge to twice that size and extend to upper leaves as spores are spread by splashing water from rain or irrigation. Plants are not generally killed, and flowers will continue to appear. Another problem in Rudbeckia is Angular leaf spot. These are two primary diseases that cause black-eyed Susan leaves to get black spots that progress to black blotches and sometimes totally black leaves.
Management for both Septoria leaf spot and Angular leaf spot are the same. Plants are not usually killed but can die back to the base. To manage these diseases, do not water overhead. Keep plants thinned so they have good air circulation and dry quickly after rains. At the end of the season (or earlier if the plants look dead), remove all infected plant material and discard in the trash so that infected material will not reinfect them next year. You can spray with a fungicide containing copper for Septoria (a fungus.) You can use a copper-containing bactericide for Angular leaf spot.
The variety 'Goldstrum' is notoriously susceptible to angular leaf spot. If you have this variety (it sounds like yours are highly susceptible), consider replacing with resistant varieties.
The native Rudbeckia hirta (short-lived perennial) is highly resistant and seeds itself so freely that it's like having a perennial plant.