Episode downloads vanishing

On my iPhone the podcasts app says it has downloaded podcast episodes but when I try to play them back while offline or restart the app the episodes are no longer there. If I look at the downloads in progress I can see them happening but the downloads vanish immediately.

How can I fix this? It works fine on my iPad, seems to be something specific to this device. I tried deleting the app and data and also reinstalling the phone from backup but neither has resolved the issue. Downloads of other media (eg, music and videos) seem to work fine.