EvalScript is known to be flaky and should be avoided.
Can you not poll your other machine using getNetText or similar? If you really need to have the browser communicate with an embedded Shockwave movie (and it sounds like there might be a better option), take a look at this demo by Valentin Schmidt (which doesn't seem to be working for me with the current version of SW in Firefox/Windows)
He also has a SOAP example, socket example and http server push example available.
I tried your suggestion first, using getNetText to poll the server and read a text file. The drawbak is that I had to poll the server constantly, since I could not know in advance when the text file was going to change (and it's not practical to stump the server and connection).
I've got it working now. I used the console in Chrome to check the shockwave object and its methods; the script is exactly the same as above with one difference: the call to EvalScript was made using the name (ID) of the shockwave object, and the function name is "EvalScript()" (not "evalScript()").
(EE02 is the ID of the shockwave object).