trouble with podcasts not downloading when it says it has

I live waaaay out in a very rural area where there's no cell service for miles. If I'm going to drive somewhere I have to make sure my podcasts are downloaded over my home wifi before I leave home. While my Podcasts app tells me that they are, they actually aren't, as I sometimes discover when I try to start a new episode and suddenly it's not there. I've been through all the settings and can't figure out what I'm doing wrong. For instance, when I tap on the three dots and a menu shows up that says "remove download" I assume that means it's been downloaded. But when I actually try to listen to it, it's not there. Any thoughts? iPhone SE running 15.4.1.