I use podcasts every single day at work and it always remembers exactly where I'm at in podcasts I'm listening too. It takes about an instant after I open the app but the bottom control bar pops up with my last listened podcast with progress saved every time.I fucking despise the Podcast app redesign. When you start a podcast, instead of it immediately taking you to the screen with all of the relevant controls (15-second skips, pause, etc), it just displays a tiny little interface at the bottom of the screen that you have to touch to reach that next screen. They've also removed the "Currently Playing" option that would take you to whatever podcast you most recently had on. So no if you get halfway through a podcast, pause it, and then later want to resume it, you have to actually look for it, which is a big pain in the ass if you have multiple podcasts, each with multiple unplayed episodes.
On top of that, it's also removed a few of the artwork icons some of my podcasts had.
Garbage.
If I switch podcasts or listen to a different episode, it still remembers where I'm at in each episode
Are you sure there's not a setting you have turned off somewhere?