I haven't checked Kazzalite, but since the same problem has been encountered with Kazaa some time ago, I think the reason is still the same.
The avast! resident protection (more precisely, the Standard Shield) works by "hooking" some functions the applications use to work with files. It means that whenever a program is accessing a file, avast! resident provider is called first and (after scanning the file) it will either allow, or deny access to the file.
Kazaa executables are packed with various exe packers. Well, why not. Unfortunatelly, some of the executables are packed using rather a nasty packer, with absolutely ridiculous settings. When you start such a program, it will try to detect any modifications to the file, any debugger running, and also any hooks present. If such a hook is detected (which is a case when the avast! resident protection is running), the program will INTENTIONALLY CRASH ITSELF.
So, that's it. When Kazza finds avast! hook in memory, it will crash - on purpose. Finding it extremely stupid? (Just the fact that this is an official forum prevents me from using a much worse adjective.) As usually, such a "protection" only bothers completely legal users (if anybody, for some completely unkown reason, really wanted to modify the Kazza executable somehow, he would find a way).
Since the problem you describe concerns Win9x only and since until now, only Kazza has been found to use this paranoid packer & settings, I'm not sure whether this problem will be addressed anyhow - it would require non-trivial changes in the avast! resident protection implementation, which might result in more problems elsewhere in the end.