I had a similar problem in Elyssa. I just did a fresh install of Felicia (Main Edition) and things are now slightly different.
First, instead of a blank grey box, I get a box that replaces part of the original Flash video frame and has one of those spinning updating GIFs in the middle.
Second, and more importantly, the blanking out is occurring MUCH more often. When I was on Elyssa, Flash videos would turn into grey blank boxes if I'd been using Firefox for too long or had too many Flash videos open at one time. Now on Felicia, nearly every video I look at dies at least once while I'm watching it. I just installed an update to the flashplugin-nonfree package today hoping it would help, but no dice.
Any advice on how to make Flash more stable in Felicia (or Linux in general) would be GREATLY appreciated. Thank you!