My cup flower plant (silphium perfoliatum) comes up healthy in the spring but as it grows the leaves begin to turn brown and very brittle. This continues all summer, even whn the plant is in full growth and blooming. I have tried moving its location but that did not help. Photos attached.
It has a fungal infection that is being spread to each area that it is moved. You will want to correct that.
Use DOLOMITIC lime and WETTABLE sulfur together according to the package instructions. These two together will kill off the infection, as well as recondition the soil back to its proper pH.
See the link at the end for common pests of cup plant. Many are native insects and an important part of the ecosystem. Did you know that most birds feed their nestlings insects, even the birds that come to our feeders? Another cause is sometimes called senescence; the lower leaves get old and become shaded out by upper leaves. They may yellow, shrivel and die. Check for pests but this may be natural on this plant. Have you grown sunflowers: they do the same thing. I remove leaves that are not mostly green to reduce the risk of disease and to make the plant more eye appealing. The fact that your plants go on to bloom well indicates that this isn't a serious problem; instead, it is more of a nuisance. https://www.canr.msu.edu/nativeplants/uploads/files/Cup_plant.pdf
can I take seeds now and plant them for next year
Wait till the seeds are dry and then plant. They need three months of cold, moist weather outside or in the refrigerator if planting in the spring. Here is more:
https://www.wildflower.org/plants/result.php?id_plant=sipe2
https://www.gardeningknowhow.com/ornamental/flowers/cup-plant/cup-plant-information-how-to-grow-cup-plants-in-the-garden.htm