If you control the protocol (that is, both the client and server) I would highly recommend using Javascript/JSON for your server-to-client messages. The client can open a stream either via dynamically adding a <script> tag to the DOM. The server can then send a stream of Javascript commands like:
receiveMsg({type:"text", content:"this is my message"});
Then the client just needs to define a receiveMsg function. This allows you to rely on fast browser code to parse the message and determine where the end of each message is, at which point it will call your handler for you.
Even if you're working with an existing HTTP protocol and can't use JSON, is there some reason you can't use XMLHttpRequest? I would expect it to be more stable than some poorly documented Firefox-specific XPCOM interface.
--Chouser