Do you have the annual or perennial Cosmos? Both will lose all top growth, the annual Cosmos not regrowing.

I have a Chocolate Cosmos which is perennial but only half hardy. It is coming in this week, but all my others are annuals, as Kildermorie says, so I just leave them to die off where they are. Shame, but it will soon be planting time again. :o))

they are so easy to grow from seed in the Spring and 1 packet gives loads of plants