BBC iPlayer picture becomes jumpy for downloaded programmes

I use the iPlayer to download programmes onto my Mac. The picture starts off fine, but seems to get very jumpy after a few minutes. If I pause the programme and leave it for a few minutes it runs smoothly again for a little while. I assume this is a RAM problem. I have a pretty large amount of RAM, so wouldn't have expected to have such a problem. Any ideas on how to keep the picture moving smoothly throughout the programme?