Ummm, I've recorded a lot of sermons. There are a variety of ways to do it. One option is to run the SBD line out through an interface (Focusrite 2i2 works well) directly into a computer running Audacity (free). Then no batteries are involved. Install this package, and do your compressing after recording:
http://acoustica1.cachefly.net/other/Classic-Effects-Installer.exe. The compressor in that package works very well.
I wouldn't install an external compressor because people have a tendency to twist knobs a bit more than they should, and then you end up with live audio problems and a bad recording, too. You just have to dial the pastor in so he doesn't clip or ride the fader on his mic.
If there is some reason to have an external recorder instead of an interface/computer, the Sony M10 has excellent battery life and is a very fine recorder. You could probably run it all week on a good set of batteries. You can hook it up to a PC via USB cable and download or put the microSDHC card into an adapter and download from that.
A lot of the poor sermon recordings on the internet have to do with reducing the file size too much so the sermon will download onto places like sermon central. You need a good quality recording to start with, and then don't reduce the file size too much. That will ruin an otherwise listenable recording.
Some pastors pause too much, and for internet listening, I usually boost the playback speed about 4% to compensate. There's feature in Audacity that will allow you to boost the playback speed without increasing the pitch.