I talked to my host, and they’ve disabled it on their shared servers. They suggested I add the following code to the functions.php and that seemed to do the trick. (Add it to the very end of the file.)
<?php
function block_transport() { return false; }
add_filter('use_http_extension_transport', 'block_transport');
add_filter('use_curl_transport', 'block_transport');
add_filter('use_streams_transport', 'block_transport');
add_filter('use_fopen_transport', 'block_transport');
add_filter('use_fsockopen_transport', 'block_transport');
?>
