I've been running into a situation where nearly every time I try to debug my app, the browser hangs on the Flash "loading" screen.
With Flex Builder you can stop the debugger and it kills fdb, un-freezing the browser, and then you can use your app and browser again, but without the debugger.
With IntelliJ pressing "stop" doesn't seem to kill fdb, so then I have to go into Task Manager and kill fdb myself.
Based on the bug reports on Adobe's site the problem occurs when your app tries to make a connection back to your local server (127.0.0.1), and somehow that stops it from also connecting to fdb. They say it's been fixed but not released to the public, so if this is hurting your productivity you might want to go watch it on their Jira so you will know when they release it:
http://bugs.adobe.com/jira/browse/FB-16153
They promise to post to the bug report when they make the release public.
The only workaround I know of is to use Flash Player 9 instead of 10. For me 9's debugging works fine every time and my project doesn't require 10, so I'm good to go. For my co-workers that require 10 though...