With Stitcher, you can download episodes to listen to even when you do not have an internet connection
To enable any of your shows to download for offline listening:
Click on the gear icon in the top left corner to go to Settings
Under “Download Settings”, click on “Auto Downloading”
Select “All” or any show you’d like to auto download the newest episode
Note: You can limit the number of episodes by going to the Show page, clicking on the gear icon and setting the maximum number of downloads to keep.
You can also download a single episode of a podcast by tapping on the episode title and choosing “Download” next to the play button. All downloads can be accessed in the section “Downloads” that is on the “My Podcasts” page.