Hello Corbella,
Thanks for the question. After reviewing your post, it sounds like the Podcast App is not saving the playbac position. I would recommend that you read this article, it may be able to help the issue.
Podcasts for iOS: Sync podcasts - Apple Support
Podcasts can remember your playback position between devices and computers, so you can always start where you left off. If Sync Podcasts is on for your iOS device, playback position will sync. However, you might need to turn on this setting in iTunes on your Mac or PC.
- Select iTunes > Preferences.
- Click the Store tab.
- Select "Sync playback information across devices." It may take a few minutes to sync.

Thanks for using Apple Support Communities.
Have a nice day,
Mario