Stop iTunes from automatically stopping podcast downloads
You cannot get iTunes to stop doing this, sadly, and I don't think you can exactly re-implement the Doug's Applescripts solution for expired playlists for Windows - it relies on manually updating each podcast rather than calling update all. And the iTunes COM object does not seem to expose a way to update individual podcasts, only the entire list.

And I am 99% certain that Matthew is incorrect and that refreshing all is not sufficient to bypass the recently listened count. The wperry link will mark the podcast as listened to, which is the same issue as your workaround that you find unacceptable. 

I do think, however, that you can workaround this issue by right-clicking and choosing refresh. While that's unnecessary to actually get new episodes when you have periodic updates set, it will reset the clock, as it were, and prevent it from stopping when you don't listen for a while. Whether this is actually any better than just dealing with it as it comes up, however, I don't know.