Annie, the spores do not persist in the soil or in/on dead foliage for the duration of a winter where all the foliage dies back. The only spores that persist through the winter are the teliospores (winter spores) but they cannot re-infect daylilies, only patrinia. Usually in your zone the reason rust re-appears the following year is from new plants, or plants kept in a greenhouse over winter. It could theoretically also survive under a winter mulch that keeps the leaf bases green.
Sharon, I'm not sure if you were thinking dusty miller could pass rust to daylilies, probably you were not because it doesn't
