It is in fact a networking issue. For instance, if you're using a VPN and the podcast server doesn't like you for any reason, such as being "out of region", or simply that you're using a VPN and they don't like that (who knows), then it can and will disconnect from your client. In my case, disabling the VPN solves the problem. However, now you're naked on the Internet. Once I've got the stream connected, I immediately reconnect VPN and I feel better.
What IMO Apple ought to fix (admittedly running Monterey OS on a 10-yr-old Mac) is, once you get the error and podcasts app displays the popup, you're stuck in an infinite loop (pardon the expression), clicking "OK" only for the app to retry the connection, bringing up the same error over and over. There's no "Cancel" option. You can't quit from the dock. You can force-quit, but c'mon guys!