Had to register to come and announce I have the exact same problem.

All twitch streams reload every few minutes for me. Downloading certain (100% trusted and legit) files stop downloading completely, I have to pause and resume the downloads to get them to start again.
Everything works 100% perfectly without webshield.

Using Firefox v24 on Windows 7 Home x64 (tested all this stuff without the online security plugin, no effect. Only Avast WebShield makes everything reload).