To all those whose problem is not lack of space (I had > 14 GB free) and is not fixed by a reboot, I would suggest taking a look at the following Preference setting in iTunes on your Mac. (I currently have iTunes 11.1.2 (31) on OS X 10.6.8.)
1) In iTunes, go to the Store menu and Sign In with your Apple ID, if you are not yet signed in.
2) Go to the iTunes menu -> Preferences... -> Store Preferences -> Sync podcast subscriptions and settings
If this setting is checked (i.e. On), then uncheck it to turn it off. (You may still need to reload any saved podcasts on your iPhone that are already corrupted, either using Add Old Episodes, or by going to the "i" information on the corrupted podcast, choosing to Remove Download, and then choosing Download Episode. If you can't download the podcast again, you might see if there is an Undelete utility for your device that could find and restore the deleted file. I don't know if that is available for mobile devices.)
Notice that this setting is not the Device setting that has been mentioned earlier in other posts. I have a couple reasons to suspect that this setting may be a key factor in the problem, at least for some people.
For me, everything worked fine even after upgrading my iPhone to the new operating system -- as long as I was using the podcast that had been set up originally in iTunes on my Mac. The trouble started *after* I added a new podcast directly on my iPhone, which meant that its settings had to be synced with iTunes on the Mac. At my next sync with the Mac, the sync did not go well and subsequently the saved podcasts on my iPhone were corrupted as described.
It was after making this Preference change that the problem has disappeared for me. I can have different settings between devices for my Podcasts (e.g. on my Mac, going to Podcasts -> select one -> Settings -> unchecking Subscribed and setting Download to Off). Yet, while there is no longer any syncing of the settings, the saved podcast recordings still do sync between my iPhone and my Mac. New episodes downloaded to my iPhone are synced to my Mac. Adding old episodes on my Mac will sync them onto my iPhone. But with no problems of corrupting my saved podcasts -- even if they have never been listened to at all. (No need to listent for just a couple seconds to keep them safe.)
There could be different causes for similar symptoms such as with this "temporarily unavailable" issue. I hope this solution helps some others who have not found the other solutions to work for their situation.