One of my fellow agents told me I was offline but my console was showing that I was online. To me, he appeared offline. I tried sending an agent-to-agent message, but he didn't receive it. I decided to exit the program and start over. When I did, the program hung with the infinite spinny wheel, and I eventually used End Task to kill it. When I logged back in, I got a prompt to enter a code using my Authenticator app, so it appears that what happened is my company SSO connection timed out.

We're going to try setting our SSO timeout to a very long time to avoid this (we'll see if that works or not), but regardless, if I'm not connected, the console should let me know that I'm signed out, rather than letting me think it's business-as-usual.