Why do people pass out after donating blood when they have fasted? 

I've worked in a blood bank. Not many people passed out while i worked there, it's quite rare, but for those who do, not eating/drinking enough (normal amounts) was the most common reason besides beein nervous..

If you haven't been drinking enough your blood volume falls. The fluid in your blood (plasma, mostly water) needs refill all the time, if not, it will "drain" (sweat, urine, etc).
When the blood volume falls, the pressure falls. To prohibit this, the veins in your body constrict. That makes the volume of your veins to fall and the amount (volume) of blood has the same ratio to vein-volume, and the blood pressure is unchanged. If you're dehydrated the veins have constricted to try to keep the pressure up. If you add blood-donation to that, the volume falls even further. The veins can only constrict so much, and it might not be enough to keep the pressure at a normal level, you might start to feel dizzy or even pass out if you are dehydrated enough.
Sprinke that with a little nervosity that makes the veins expand (dilate) and that makes the pressure fall even more. The brain doeesn't get enough blood, and you start to feel dizzy and eventually pass out.
You should allways drink a good amount (0.5 litres) right before/during donation, so your stomach holds enough fluid to readily replace the fluid loss of donation.

As i said to begin with, people passing out was rare. In the few cases when people started feeling dizzy (mostly first-time donors that had been thinking about it and worrying a lot before the donation), we could either instruct them to drink more, lay the chair down with the legs high (makes the blood, wich follows gravity, flow to your brain and keep the pressure up) or simply abort the donation and try again some other day.

Credits: Henning Andersen