Make sure to remove the app from the device 'optimized apps' list to fix this.
You will find this in the device battery saver screen' menu.
Google fixed this bug in May 2016 and Samsung devices seem to be the only devices affected by this.
The bug fix has been embedded in Android N.
Hopefully, Samsung will backport this fix in their next Android 6 ROM update.
In the meantime excluding Podcast Addict from the 'optimized apps' list and/or downloading the episodes first should fix this issue.