I'm afraid that there's little you can do, aside from restarting Firefox. I have also experienced a similar problem, for a very long time. Whenever I play a flash-based file, I lose the sound notification in my Gmail Notifier Firefox add-on until I restart Firefox. I can continue to play flash-based content just fine, but it locks up/makes all the rest of my sound notifications inoperable until Firefox is restarted.
It's truly a shame that Adobe has put so little effort into a decent flash player for the Linux platform. It tends to be as sloppy as the rest of the stuff that Adobe has chosen to put out in the last few years.