A. Check if there is an option in the app settings to enable 'Resume Playback' or 'Save Last Played'. If available, toggle this option on. This may help the app remember your last podcast when you reopen it.
B. As a workaround, you can manually note the last podcast you listened to and search for it when you reopen the app. Alternatively, create a playlist of your favorite podcasts to make it easier to access them.