Reloading Flash 17 times causes error #2046 and requires a browser restart
Disclosure: I am a Flash Player Developer at Adobe.
This is unlikely to get much attention as it is Linux only and kind of an edge case: Probably annoying during dev work but very few users will reload the same page more than 16 times. It might also be a browser issue. But it is probably us :) I will look at the jira tomorrow and see if I can bump it up a bit, but I'll be honest in that it is really an edge case and unlikely to get much love. If you want to increase your chances make sure to add the most simple .swf test case you can make to the bug. Also please double check if it still happens with the latest beta.
I also just took a look at the earlier bug reports and forum posts, you probably should post this as a Flash Player bug, not as Flex.
Long shot guess, but it sounds similar to a problem we had.... in the project properties - Flex Build Path - Framework Linkage - change to "merged into code". This fixes a problem very similar to what you are describing, though I wish I knew exactly what the cause is. Good luck!