Try Pocket Casts too, much better for makingsure your regular Podcasts are downloaded before things go offline.
I tried switching to Apple Podcasts and I found out the hard way that it didnt download my episodes before a 10 hour flight.
Apple Music is bad with this too. Even though it's what I use for streaming, I simply do not trust it to keep things locally if it decides it might have a better idea about whether I need disk space than it does. I use Castro for podcasts (inbox/queue works great for maintaining local downloads) and Doppler for music.