A few things:
- You should only specify the options that you want to set. So, for instance, you don't need to have listName: $().SPServices.SPListNameFromUrl(), because that's the default.
- If it's intermittent, can you figure out any pattern? If it's only some users, then it's probably a permissions problem. I assume that all users can read from the relationshipLists?
- If it isn't permissions, then is your call to newServiceRequestInit(); inside the $(document).ready()? I can't tell for sure, but as you say, you may have missed a bracket or parenthesis.
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Finally, check the results coming back with Firebug or Fiddler to see if you're getting the values back that you expect when you change the parent value. It could be that something about your list structures isn't right (though it looks like it probably is).