A satellite *is* falling. It is just falling around the earth. It's hard to explain without a phyiscal diagram, but if a satellite stopped moving it would fall right down. Think of it like this.
When you throw a ball, it moves in an forward and down (from gravity) at the same time. But imagine now that that ball is throw and with so much force, that it can't fall down because gravity is changing direction as Earth's surface curves. That is basically what a satellite is. However, the force of gravity from Earth is slightly less up at that height.
Good question.