I don't know if this is a possibility for you but...
Rather than trying to update a file on another server, especially something simple like a txt file I would have the current file on server one and then I would copy it to server two from server two with cURL using a cron job set to copy the file every x minutes.
$ch = curl_init();
// set URL and other appropriate options
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_HEADER, false);
curl_setopt($ch, CURLOPT_BINARYTRANSFER, true);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
set_time_limit(3600); # 5 minutes for PHP
curl_setopt($ch, CURLOPT_TIMEOUT, 3600); # and also for CURL
$outfile = fopen( $dirname, 'wb');
curl_setopt($ch, CURLOPT_FILE, $outfile);
// grab file from URL
$response = curl_exec($ch);
fclose($outfile);
// close CURL resource, and free up system resources
curl_close($ch);
`
I would do this just because you would not have to deal with setting up a FTP account for the update or anything like that. Your server that you need the file on is going out and grabbing the file for itself.
I use the above script to collect mp3s from various blogs. Sometime they will be 100-200MB and it works fine running off a shared server.