I also have the same problem! I have an iPhone 5 with the most up to date IOS Software and have subscribed to Spotify Premium. My podcasts constantly delete and I have to redownload them daily. If Spotify does not fix this glitch soon it will make me consider switching to a different streaming platform as I use these podcasts as a way to keep entertained on my 3 hours of commuting daily! I also subway so I do not have access to use my data to stream these podcasts. Additionally, why are podcasts unavailable on a computer or laptop when using the app?
Having the exact same issue. On top of that there is now download progress indication for podcasts, as there is for music. If I click "Download" the indicator turns green instantly as if the podcast was fully downloaded in less than a second, which it is not.