Yes, it seems like Firefox kills the flashes instances that are not visible.
I had the same problem in Firefox 3.6.13 and Flash Player 10.2.152. I tryed with "visibility:hidden" and "position:absolute" but didn't work even with "wmode=opaque".
For me the solution was setting the "wmode" to opaque, "position:absolute" and "opacity:0", but it´s not possible to set the "top" property to negative or whatever "position", "overflow" or "margin" hack. The entire movie need to have its "space reserved" in the page to avoid Firefox killing it.
I needed to toggle the visibility between two flash movies with the same size, so, the solution was setting the opacity of one of them to 0 and changing their z-index properties to put forward the active one. It worked fine.