I have a huge issue with this on my Galaxy S3 - so much so that I purchased a Razr Maxx HD to use until I sort out the problem. This has only been a problem since the Jelly Bean OTA. I have factory reset my phone 3 times, reformatted the SD card, tried a new sd card, tried NO sd card, and the problem persists on reboot. If I force stop the "Downloads" app (process?) then it stops until the next reboot. Better Battery Stats tells me that I have a MediaScannerService partial wakelock - and that's why my battery is running down. The phone never gets to sleep.
Anyway, I know that you problem is on the RMHD, but it might be the same issue. Try force stopping Downloads, and see if that helps.