What this message means is that some time after your module has started up the render process loses contact with it. "Crash" is a little too specific of an error message, you may have hit an assert, or the program may have called exit(). I personally haven't developed on Chrome OS, so I can't address the particular debugging limitations you are working under, but I can outline how I'd deal with the problem on other platforms:
There are env variables to redirect NaCl's output to files (NACLVERBOSITY=0/1/2, NACLLOG=file, NACL_EXE_STDOUT=file, NACL_EXE_STDERR=file). Prefer using absolute paths, Chrome interprets relative paths is a way that is slightly counterintuitive. (Relative to the Chrome executable? It's been a while since I had to deal with this.)
If redirecting to a file is a problem, see: native_client/tests/postmessage_redir/ for a way to send stdout to postmessage. The downside is you'll still need to sent an environment variable (NACL_EXE_STDOUT=DEBUG_ONLY:dev://postmessage) and if you're using postmessage as part of your app you'll need to sort through the stdout spam. If setting environment variables is a problem, we'd need to talk to the Chrome OS folks and see if they have any debugging tricks.
Please keep us updated. It would help us to have feedback on where the rough spots are when debugging on Chrome OS.