How to get iTunes to keep downloading podcasts even if I don't listen to them right away?
Apple covers this feature in their Making a Podcast page.


  Automatic Unsubscribe.
  
  iTunes automatically unsubscribes from
  a podcast if the following conditions
  are both met:
  
  
  The user has not played any episode downloaded in the past 5 updates
  (there may be more than one episode
  downloaded per update.
  More than 5 days have elapsed since an episode was played.
  
  
  In addition to minimizing unnecessary
  bandwidth costs for both the user and
  the podcaster, the unsubscribe logic
  built into the iTunes client makes it
  more likely that episode downloads, as
  reported by a podcaster to a sponsor,
  are roughly in line with actual plays
  of the episode


And as far as I am aware, you cannot disable this feature.