I would try adding a date header to the emails. Open class.email.php, and find:
$headers = array ('From' => $from,
'To' => $to,
'Subject' => $subject,
'Message-ID' =>'<'.Misc:(6).''.time().'-'.$this->getEmail().'>',
'X-Mailer' =>'osTicket v 1.6',
'Content-Type' => 'text/html; charset="UTF-8"'
);
This occurs twice - about line 161 and again at about 219. you will need to modify both so that the end of the code looks lie this:
'Content-Type' => 'text/html; charset="UTF-8"',
'Date' => 'date('l jS \of F Y h A')'
);
You may need to play around with the format of the date, so that it matches exactly what outlook is expecting.
Let me know how it goes.