The short version:
When using The Events Calendar PRO (having installed it, as well as the standalone version of the TEC, and disabling the built-in version), there exists an issue which causes some of the pretty permalinks for the sermon content type to not work. I believe I have tested every possible configuration to demonstrate that the issue is between the latest version of TEC and the Incarnation theme. Details below :-)
The long version:
The error can be seen on both single sermon and sermon category pages, though the full sermon archive works fine.
Example problem links giving 404 errors:
I have installed the Pro version of the Event Calendar, which required me to also disable the built in event calendar plugin so that I could install the current version of the base plugin. I commented out the code as described in http://www.kriesi.at/support/topic/need-help-on-pro-version-of-calendar#post-88156
The problem does NOT exist when using the built-in event calendar plugin.
The problem does NOT exist when the permalink settings are set to default (this suggests to me that there is a rewrite conflict perhaps?)
The problem DOES exist when all other plugins are disabled.
The problem DOES exist when TEC (standalone) is installed without TEC-PRO.
The problem DOES exist after flushing the rewrite cache.
The problem DOES exist after re-saving the permalinks settings.
The .htaccess file is writeable and has not been altered.