A FAQ helped!
I just started playing with the Swell app (http://swell.am) but was annoyed that whenever I switched apps, it paused. Then my phone timed out and locked, and Swell stopped. That moved it from annoying to useless.
So, before I dug into support and Twitter, I read the FAQ. And found this:
I'm having issues listening to Swell in the background or from my lock screen. How can I fix this?
If you run into this issue, please try restarting the Swell application. We apologize for the problem and are working on a fix.
Yup! Problem solved. Works like a champ now. Funny how documentation can be helpful...