I was in the same boat until a few weeks ago...(carefully staying on the old version of AIR)
During which I repeatedly ran into the same problem of "A problem occurred while downloading this program" about 999999999 times....
I tried the old method of deleting the roaming data etc. every time seem to bring it back to life for a bit...before it start playing up again.and again
(I even download a few programs I know I wont cry over if i cannot load it as a test file...if it does not load time to do the trick...)
However there was one time i must had got the order of deleting restart iPlayer wrong and i lost every single video downloaded. (was moving repository but it did not copy over i guess)
since I cannot lose anything more i went and upgraded AIR into version 3.60.5970 (with BBC iPlayer 3.2.15)
and iPlayer seem to be............
still in the same mood. "A problem occurred while downloading this program" is backkkkk (just now)
oh well!(back to deleting roaming data now and then)
I can only say:
When you have time just watch whatever you downloaded as soon as possible. Don't hang on to it...priorities your programs' worth watchingness...
I wont cry if I cannot load certain programs because there is always a way if there is a will
but some programs worth watching because they are HD or its not possible to find it again until they bring it out as box set...then watch them!
Cannot believe BBC force me to priorities during my spare times but what the heck...