This is likely the result from various leaf-spotting fungi (including Septoria) that commonly infect Black-eyed Susan foliage. They may weaken plants after successive years of leaf-kill, but otherwise do not cause serious harm. Diseased leaves can be removed as they are spotted, and all debris should be cleaned-up at the end of the season after frost and disposed of to limit overwintering spores. Plants in full sun (at least six hours daily in summer) are less vulnerable than those growing in more shade; they will also flower best. Using a mulch over the soil (though not touching the plant's base) will help reduce plant stress from evaporation of moisture, soil temperature swings, and weed competition. A layer no deeper than three inches will be sufficient, though it can be thinner.
If the plant is in a good location (full sun, good soil drainage) then you could consider the use of fungicides next spring. We do not normally recommend them as over-use may have negative effects on pollinator and soil microbe health; additionally, not all fungi are well-controlled with fungicides, though their severity can be tied to weather conditions which influence their spread or plant stress. They will only work preventatively with regards to plant diseases and are not curative, so treatment once plants are symptomatic is not practical. If you try one, a registered fungicide (meaning, not a home remedy but a product labeled for this use) that lists "leaf spot" on its label (and Rudbeckia, though it may not get that specific) may be worth trying; follow label instructions about application timing and frequency.
The alternative is to replace the plant with a different cultivar or species of Rudbeckia; not all are highly prone to contracting disease. The commonly-used cultivar 'Goldstrum' seems to be one of the worst with regards to vulnerability, where even its parent species, Rudbeckia fulgida, appears to be relatively more resilient.
Thanks so much for all the good info. I would like your thoughts on my idea for the bed. Remove all the old plants and the first couple of inches of soil (the soil there now is not rich & loamy ... it's very much clay-based). Then add a mix of garden soil, LeafGro, peat moss and top off with mulch. Let it lie fallow all winter then in spring pland Rudbeckia fulgida. Would there be any benefit to applying a fungicide to the old soil before adding the new mix? Thanks, I look forward to your advice.
If you are taking out the plants, you do not need to remove the soil unless there was evidence of the disease Southern Blight (which we don't see here). Mixing-in a little bit of compost (like LeafGro) is a good way to mitigate compaction and improve drainage. Peat moss is not necessary and may not be beneficial, though mulch over top of the soil after planting is fine. It may not hurt to leave the area fallow but it's probably unnecessary; fungal spores of common diseases are ubiquitous in the environment and can re-appear at any time, though their impacts can be quite weather-dependent. Drier springs, for example, will probably see less incidence of disease. (Similarly, if you happen to use a sprinkler system, it can promote disease if run too often.)
There is no benefit to using a fungicide on the soil itself; it may even harm beneficial soil fungi, though we do not have research that demonstrates specific impacts. Rudbeckia fulgida is but one option; if you want to stick with Rudbeckia, there are other similar species like Rudbeckia triloba or Rudbeckia hirta, the latter of which is our locally predominant native species.