@ww2_1943 My guess is that the version of WebKit embedded in iTunes uses too old a version of TLS to establish a connection to the podcasting site, or at least the domain on which the media file is hosted on. So while maybe it can connect to and then display the podcast list (TLS requirements meet eye-to-eye), the hosted file locations have different requirements (for some silly reason).
But that is only speculation. Assuming that were indeed the case however, you might try using the Wayback Machine as a proxy for iTunes to connect to instead of the site directly (akin to as recently detailed in
the TLS 1.3 thread), but save for that, there wouldn't be anything else you could do. But once again, that's all speculation surrounding the vague reasons why iTunes isn't fetching the files; it could also be something else entirely.
Now, with that being said ...
If you have both a sustained drive and unfailing patience, you can do anything. Or to put it another way,
determination + time x resources = results.
Just ask questions of how things work, and how exactly resource-rich corporations like Apple assembled a piece of software such as (or more relevant, a cohesive user experience like that offered in) Mac OS X. Wherever possible, use the same tools that they used for their own products, and continually refer to a base idea or collection of wishes for guidance in which direction to progress. And you must exist in an endless state of learning, because you never know what you might add to your arsenal along the way.
I hope that was helpful.