I think obfuscating software is altering bytecode. For example, addition of invalid bytecode used to break decomplilers in the past, while Flash Player still played swf correctly. This is endless battle of sword and shield (but it seems obfuscators are in better position.)
To be more concrete, if your application breaks after obfuscation - what you can do:
- exclude fragile resources like animated clips from obfuscation. If you absolutely need to protect them, you can encrypt them with simple algorythm like RC4 (it's fast) and decrypt in obfuscator-protected section (see as3crypto).
- work with KindiSoft, sending them error reports with examples of broken swf.
- add your own obfuscation methods, like hiding of logic in pictures/other resources.