Cannot upload files consistently. (BB-1276)

I'm using Firefox v3.6.13, and I am unable to upload any downloadable files consistently. In order to make uploading work, I have to try to upload the file several times in a row, by repeatedly clicking "upload" and then "Continue" when the security warning pops up. And this results in a file who's name is repeated based on the number of upload/Continue cycles I needed to press before it actually started uploading.