The Order Update email template under Configuration > Communication settings has an IF condition in the Mail To that looks something like this:
{xsl:if test="in/salesOrder/shippingStatus = 3 and in/salesOrder/previousShippingStatus != in/salesOrder/shippingStatus" }{xsl:value-of select="in/user/email" /}{/xsl:if}
It basically tells it to only issue an update if the shipping status has changed by setting the Mail To to the user's email (blank email would tell the system not to send out).
You can remove the IF condition so that it will always send anytime any of the statuses change (not just the shipping status) when you save the sales order in the Sales > Orders administration screen. It would look like this without the IF condition:
{xsl:value-of select="in/user/email" /}
I hope this helps.