BeyondPod does not pause or resume when I receive a call or notification

The first thing to check is if "Pause on Notification" is checked in BeyondPod' Settings > Player Settings > Pause and Resume.

If this setting is checked, most likely there is other application that interferes with Android audio focus. "Pause on Notification" is based on the Android Audio Focus infrastructure. Similar to the input focus, only one app can "hold" the audio focus and if another app tries to play something it takes the focus away. BP listens for this "take away" message and pauses the feedback until the focus gets back. If another app steals the focus and does not return it, BeyondPod has no idea when to pause or resume.