Your podcast Store page is at https://itunes.apple.com/gb/podcast/generation-mouse-podcast/id419621242?mt=2
Your feed is at http://feeds.feedburner.com/generationmouse
(Please always post these when you have a query to save detective work).
I subscribed to your podcast and was able to download and play the latest episode without problems. I also was able to start playing several episodes fro the Store page.
I don't have an iOS device so I can't check it on that. However your server (Archive.org) appears not to support 'byte range requests': this is the method whereby only parts of the file are requested at a time instead of the entire file, and is how the iPhone downloads podcasts. If the server does not support this downloads on iPhones are liable to be problematic.
However your complaint seems be that it's not the iPhones which are causing the problems but when subscribing in iTunes and I can't reproduce this fault lon a Mac.