It happens with IE too.
What does the iPlayer use? Just flash?
( Master Of Turnips. Only gays and morons believe in ghosts., Mon 18 May 2009, 20:49, archived)

flash and a javascript library to load the flash
Its a pretty robust bit of kit and I would suggest it might be something on your end. Like the version of flash.
( MrA, Mon 18 May 2009, 20:51, archived)