When the log file is rotated, it is being renamed.
The fs.watch function in node.js has the ability to notify you when the file changes.
http://www.nodejs.org/api/fs.html#fs_fs_watch_filename_options_listener
Try something like:
fs.watch('filetowatch', function (event) {
if (event === 'rename') {
// close the file descriptor you are reading from and re-open.
}
});