I sent and email to Pandora last night regarding this problem and today I received a reply from Josh:
Thank you for taking the time to write us here at Pandora and thank you for the kind words. I apologize that you are having some trouble. Our engineers are aware of this issue and are working to have a fix for it soon.
In the meantime - You can coax the music into playing again by pressing the pause/play button twice, or by skipping (although pause/play is preferred because you won't use up a skip). It's not an ideal workaround, because it means you can't have unattended play - but it might help in the meantime.
We appreciate your patience in the meantime. Thank you.