I have two flash movies, on different tabs of a user's browser.
They use LocalConnection to talk to each other, but the one on the tab which isn't active doesn't do anything until you switch back to that tab, can you change this? Maybe in the embed tag?
One of the things that Adobe changed about the Flash player after 10.1, in order to make it consume less CPU cycles was to force the player to only execute at 2fps (or some other ridiculously low amount) when the swf is no longer in focus (or even if it's still "in focus" but not being rendered to the screen by virtue of being in a section of the browser window that's scrolled offscreen.
I'm not aware of anything inherent to the new Flash player that would prevent LocalConnection from working, though. Do you have listeners set up to detect whether the swfs in question are active or not before they attempt to make any calls?