You didn't specify what error or exact problem other than saying it didn't work.
Well, I do not see a problem with your use of DATEDIFF() unless you don't have MySQL version 4.1.1 or higher. So, if you don't have at least that version, then I recommend you use TO_DAYS() SQL function instead. Example:
$dateQuery = "SELECT loan_client_ID FROM loan WHERE (TO_DAYS(CURDATE()) - TO_DAYS(loan_date)) > 2678400 AND loan_client_ID = {$row['client_ID']}";
If you're getting "Could not retrieve loan dates", then also display what the error is using mysql_error() function.
If you want to do it in PHP, then here's an example (I'm assuming date is in YYYY-MM-DD format):
if (time() - strtotime($lrow['loan_date']) > (60*60*24*31)) { // 2678400 seconds (31 days)
}
Let us know how it turns out.