You can listen to your favorite podcast shows offline if you download the episodes. If you do not download the episode, you will be unable to listen offline.
If you close the Medscape app, you will still be able to listen to a podcast episode. The audio player will continue to play in the background. However, if you force quit the Medscape app, your audio player will stop playing. To resume listening to an episode, reopen the Medscape app and find the episode you want to listen to.