Hmmm.. Never had that happen. I use rapidshare to host large home video files to share with family and friends. They do the same. I've been known to download up to 12 files, 100 or 200MB each, simultaneously without problems.(using firefox browser) I've heard of, and seen for myself, some problems that can occur, but never what you described. It very well could be a wireless issue but that's pure speculation.
Do you have this problem downloading files from any other source? You might want to find out. Also, are you using any so-called "download accelerators" ? Sorry I couldn't be more helpful.