使用readfile（）无法下载大文件

I have the following code to force download an IPA file (after codesigning it with a script). It works fine with smaller files but with larger files, my web server starts returning a 500 Internal Server Error. Would someone be able to help me tweak my existing code to overcome this issue?

$time = md5(time());

// Runs code signing script here
// And then attempts to initiate download

$path = "done/$time/";         
$latest_ctime = 0;
$latest_filename = '';    

$d = dir($path);
while (false !== ($entry = $d->read())) {
  $filepath = "{$path}/{$entry}";
  if (is_file($filepath) && filectime($filepath) > $latest_ctime) {
    $latest_ctime = filectime($filepath);
    $latest_filename = $entry;
  }
}        

 header("Cache-Control: public");
 header("Content-Description: File Transfer");
 header("Content-Disposition: attachment; filename=$time.ipa");
 header("Content-Type: application/ipa");
 header("Content-Transfer-Encoding: binary");
 // Read the file from disk
 readfile("done/$time/".$latest_filename);
       // header('location: dashboard.php');
   } else {
// Throwback

die("Failed. Contact support. // <p>$sign</p>");

}