When JUnit tasks get stuck in "No tests were found"

Tonight I needed to troubleshoot some Android Studio JUnit run configurations failing with "no tests were found." Interestingly, they would work fine until the user tried to run them in the presence of a compile error, at which point they would stop working until a Build | Rebuild Project, even if the compile error was fixed. It was fixed by adding a before-launch task to the run configuration that runs the clean Gradle task for the module. Later it was found that a plugin was interfering with the build process.