Eric, I pointed out in past that you have received elaborated Custom Code, which I adapted to your case because WooCommerce API is broken in this detail, and it is not Toolset breaking this API, since it does not even touch or create them
Last time we debugged this over 1,5 months to find out that the code in functions.php was not copied over to the real site and not registered.
Then we have had the same issue again, with a update of the theme and the code "stopped working":
https://toolset.com/forums/topic/conditional-shortcode-not-working-after-toolset-starter-theme-update-1-3-5/
Since this is working on your Test Server and you seem to have updated Toolset there (according your statement), as well, I assume it is a similar issue here.
I see on your Live site you use the Toolset Child theme, a outdated version.
Although as far I can see, all code is present in the active theme, and the ShortCode is registered, I see in your layouts Content Template Cell some unusual Code that I did not recommend to use.
[wpv-conditional if="( '[wpv-product-purchased]' eq '1' )"]
<embed src="[types field=" episode-pdf"="" link="true" output="raw" ][="" types]"="" width="100%" height="500">
<span style="font-size: 13px;">
<a href="[types field='episode-pdf' link='true' output='raw'][/types]" target="_blank">
<em>[wpml-string context='wpv-layout-conversation']Can't view transcript below? Open PDF in new window with this link.[/wpml-string]</em>
</a>
</span>
<br><br>
<span style="font-size: 0.8em">[wpml-string context='wpv-layout-conversation'](Note: No refund possible for the purchase of this episode)[/wpml-string]</span>[/wpv-conditional]
I do not know what your goal is with the empty apostrophes as in types field=" episode-pdf"="" ...
or in [="" types]...
This certainly is not something we provided.
When you insert the ShortCode with the GUI, as recommended, you will get:
[types field="episode-pdf" link="true" output="raw"][/types]
No spaces, no brackets, nothing unusual and unexpected.
Anyway the ShortCode evaluation is working fine as expected.
Just change the evaluation from '1' to '' and you will see your PDF Link in the Product page, means, the conditional is correctly hiding it if the product is not purchased and will show it if purchased.
Or Yin can replace your code with a OK / Not OK output to check purchased and not purchased products.
Although your code in that evaluation is wrong, it has wrong ShortCodes and apostrophes, and that will most certainly break your content.
Please fix this code according the guidelines of ShortCodes.
Thank you