MySQL/PHP Returning Blank Error Message
Doh! @jynus was exactly correct.  Here is the fix:

$eventid = intval(mysqli_real_escape_string($dbconnect, $_POST['eventid']));
$sql="DELETE FROM Events WHERE EventID='$eventid' LIMIT 1";
if (!mysqli_query($dbconnect,$sql)) {
  die('Error: ' . mysqli_error($dbconnect));
}
echo mysqli_affected_rows() . " Record(s) Dropped";