Adobe Flash Problem with Firefox

When I go to, for example, http://www.thedailyshow.com/ I can't watch a single video. A small window pops up saying:

Adobe Flash Settings
Local Storage
(the website) is requesting permission to store information on your computer.

I can either click "Accept" or "Ignore" - but it doesn't matter because no matter which I choose, this little window will NOT GO AWAY. It's blocking the video screen.

Now, I've gone to the online Flash Settings Manager at macromedia.com. Everything checks: I have "unlimited" settings for storage and "always allow" for all other pages related to this issue.

Any idea what's going on? Pardon my lack of awareness here. I posted a thread titled "Javascript links not working with Firefox - but do work with Safari " just moments ago. If this Flash issue is related to that in some way, I had no idea and apologize for not combining the issues.