Hi,
I'm having similar issues. I have podcasts set to "check for updates: On startup", "new episode action: Download the most recent one", "keep: All unplayed episodes". Since upgrading to 3.1, MB hasn't been updating podcasts on startup and needed to be manually updated, either by "F5" or left-click and "check for updates". Sometimes a single podcast would seemingly randomly update when I started MB. Also, manually updating podcasts automatically deleted played episodes, which would also have happened if MB was automatically checking podcasts. I installed the update from above (3.1.6291) but the issue still persists. On startup, the update header takes a couple seconds to show podcasts are updating. The update process completes rather quickly, a couple of seconds, and only 2 of my podcasts were updated. I manually checked for updates and the process took much longer, almost a minute, and updated another 13 podcasts. Also, all my previously listened to episodes were automatically deleted.