This isn't be a problem with rsh, it's a problem with the shell that you are using to do the redirection.
Firstly, make sure that $i does not contain spaces or punctuation, as these can get interpreted by the shell, putting the redirection to a different file.
My advice would be to try an explicit shell invocation to do the redirection. You didn't say which shell you were using, but I'd exect something like this to work:
Code:
for loop
/bin/bash -mc 'rsh remote_machine command > file$i &'
Note the single quotes, which tells the calling shell not to inline macro names or do anything fancy. Passing the -m option to Bash tells it to preserve the environment, so $i will still work.
Hope that helps,
— Robert J. Lee