If you’ve ever had this problem then you are in luck. I’ve spent about 30 min. searching online for a solution to this problem and I had to read through about 45 different forum posts before finding the right solution. The problem was that everyone else who was experiencing this issue never actually had youtube working on firefox. This is what made my situation so much different. So if you youtube was working, then right in the middle of your favorite show, it just quits, then I have a solution for you.
It’s actually very easy. All you have to do is click on the tools menu in firefox and click “Clear Private Data” or if your a keyboard shortcut junkie like me, then it’s a simple “Ctrl+Shift+Del”. When the clear privea data window pops up just make sure you check the box next to “cookies” and then click the “clear private data now” button, and voila. Your youtube will be working like new.
I hope this helps.