Podcasts disappearing from my phone

I have an iPhone 6S running 9.3.4, but I've had this issue on my iPhone 5 and on previous iOS version.

Earlier this week I was listening to a podcast in the subway (no cell service) with the podcast app running in the background while I used another app. My podcast stopped playing without prompting. When I went to the podcast app to hit "play", all my downloaded podcasts were prompting me to download them from the cloud and were no longer available offline. The app was prompting me to change my settings and enable cellular data.

Why is this happening? Is there a setting I need to change? I don't know why the app is "refreshing" or anything of the sort while it is essentially offline.

Any tips?

-a