They almost look like they've been trampled on, and then they start to turn brown from the center of the plant. They do get some afternoon sun, but they're not overwatered. We have some cats in the neighborhood. Could they be urinating on them? That's kind of what it looks like. It happens to them almost overnight, and then they're dead within a couple of days.
I think it most likely that you've got some fungal condition going on in the bed. You might want to take some soil and plant samples to the Extension Service for analysis. This link will help you find the nearest one: https://www.gardeningknowhow.com/extension-search/
This article may help you with general growing tips: https://www.gardeningknowhow.com/ornamental/flowers/rhoeo/growing-rhoeo-plants-in-the-garden.htm
I am in the process of using oyster plants for an edging for my sidewalk and need to know how to cut or take cuttings from existing plants to grow more of them.
Some plants cannot grow from another cutting. I suggest getting some root hormone and put it on the stem of the plant where you cut it and then plant it. Keep it well watered and nourished.