Gah, I figured this out. It was naturally something stupid I did when messing around with build settings after a too-late night. Here are the things to check:
- Tools >> Options >> Project and Solution >> Build and Run >> Check that “On run, when projects are out of date” is set to “Always build” or “Prompt to build”
- Build >> Configuration Manager >> Check that “Build” is checked for all of the projects you want to build for each of the configurations you need to use.