Hi Trefor, We're having the same problem on two separate Macs running Safari. Have been through deleting and reinstalling iplayer and Adobe Air, cleared my cache. Any attempt to contact the BBC disappears into a black hole. At least their bland acknowledgement now carries a date. As of 13th June 2012 they say "We believe this issue has been resolved for the vast majority of users, but as we are still receiving some reports of problems with BBC iPlayer Desktop we are still investigating as a matter of priority."
See http://iplayerhelp.external.bbc.co.uk/help/announcements/desktopdownloads_disappear - where they promise to update us when there is more to tell. Exactly the same answer is given for "Why am I not able to download programmes onto iplayer?"
Seems all we can do is keep going through the dishearteningly convoluted comments system and hope the number of contacts hits somebody's target to cause a response.