So in the farm I'm trying to deploy to, the tracing service starting logging some "failed to write template" messages. Thousands of them. Nobody was on the machine at the time. It wasn't available to anyone so it was internal to SharePoint, whatever it was. Then it suddenly turned into the "Tracing Service lost trace events" log entries. Finally, it stopped logging altogether.
I found in a forum post on MSDN that when this happens, you need to restart the Windows SharePoint Service Tracing service.
SharePoint immediately started logging the events appropriately.
I love SharePoint and I also hate it.