If this is a Basic alert, select the alert, click on Edit Alert. Select the Alert Trigger tab and deselect the "Send Alert anytime status changes" box if it is checked. Then choose the trigger and reset status conditions that you want.
If it is an Advanced alert, then on the Trigger C ondition and Reset Conditions tabs you will have to add simple conditions for the status conditions that you want the trigger and resets to fire on. For example, "Node Status is equal to Down".
Does that help?