Great suggestion! It turns out that the loopback test was failing. I had to set up my hosts file so the server could find itself.
Thanks so much!
To summarize the solution:
In podcast-functions.php, change from:
<?php if ( $audio == ” ) : ?>
to
<?php if ( $audio !== ” ) : ?>
Found out my real problem was a bug in Sermon Manager. It was not including the audio enclosure for RSS feed, so it always showed up empty in iTunes.