Have you tried to catch Throwable? This is the super super class for exceptions as far as I know. You should be able to find out what is thrown, if anything. Otherwise do you check the status of the work item save?

        IStatus saveStatus = fWorkItemServer.saveWorkItem3(parentworkingcopy, null, null,
                additionalParams);
        if (!saveStatus.isOK()) {
            return false;
        }

I am not currently checking the status of the work item save. I'll give that a try. Thanks.

Edit: Unfortunately, neither of those suggestions has panned out. Got any other ideas?

Edit 2: Actually, I just realized that the permissions error is happening long before my saveWorkItem3 operation (it occurs when tracing links). I need to put the try/catch block earlier in the code. I'll try that and come back here.

Edit 3: Looks like the catch Throwable does the trick. Stack exchange seems to argue that it's bad practice to do that though so I guess I need to do some testing to figure out exactly which exception is being thrown for the permissions error. I'll mark your answer as the accepted solution.