In our application (a game), in some cases it can't run fast enough. Obviously we'd like to speed it up, but in the mean-time when this happens it causes many problems (or if it's not causing them, the two are related). The one which is least related to our own functionality is that the built in Alert.show() method stops working. Typically the full-screen transparent box appears but not the actual popup. I believe this is down to Flex giving all available cycles to other tasks... but it's proving difficult to investigate analytically so I am happy to hear another explanation.
To clarify, core parts of Flex are simply not working in this situation. I've stepped through the code for instance where a new element is added to the screen, everything happens and the addChild() method is called on the main display canvas... but then the element does not appear. If we then disable our update loop, the element suddenly appears.
So whether Flex is supposed to run the exact same code or not, somehow it IS blocking is some strange way. As I said, even the Flex Alert.show() method doesn't work.