It was my fault.

For some of the domains I have strict HTTPS set between Cloudflare and my server. For those domains, I have a server doing proper SSL on the egress reverse proxying to other servers or containers. At some point I forgot this, and when I noticed the hostname mapped to the "other" server and corrected it, I suddenly got offline messages from Cloudflare. I corrected it again, and instead started getting timeout errors.

I checked the correct server and found another thing I'd fogotten. In a couple of cases, when I cancelled the DSL connection, this broke, because I apparently had some of those reverse proxies using the host's public IP, instead of the LAN IP. Whoops.

I found and corrected those mappings, and now those sites are back online.