Yes, too much moisture. It's likely that you're having a bad problem now, relative to wetter times, because the spores for that particular disease speceis is so plentiful, due to it's proliferation in your garden, rather than blowing in from somewhere else. Without knowing which disease it is, it's hard to know if cinnamon will help. Not a lot you can do about it in your climate, but the fact that the delosperma are growing with other non-suculent perennials or cactus that are doing well tells me that the soil and overall conditions for any delosperma will be problematic in the long run. They definitely don't want rich or moisture retentive soil, and would otherwise bloom more prolifically. Perhaps grow them in a permanent pot or trough.
