The real problem was that I had ended up generating a malformed config file (see the schema in c:\Program Files\Microsoft Visual Studio 8\Xml\Schemas\DotNetConfig.xsd) by putting configSections after appSettings. Once I put the configSections element back to the top of the config file, everything was fine again.
Disclaimer The opinions expressed herein are my own personal opinions and do not represent my employer's view in any way.