Can upward resistive force be greater than downward gravitational force? Objects falls through air, eventually it will reach terminal velocity, but why won't this upward force increase further?
 A: 
but why won't this upward force increase further?

It could do.
For example if the object falls to a region of denser air, then frictional forces will increase, exceeding gravitational forces, and the object will consequently decelerate to a new, smaller, terminal velocity.
Air resistance is proportional to velocity, for laminar flow. This is why it does not increase once a terminal velocity has been reached, unless something else changes.
A: The resistive forces are generally proportional to the speed of the object falling. So when they start falling (with initial speed zero) gravitational force will be greater than the resistive force. Eventually the object gains the speed up to an instant where resistive force becomes equal to the gravitational force and since an equilibrium is reached at that point the speed stops changing at that point - so stops the change in resistive force. (Because it is directly proportional to speed) So everything reaches a steady state and objects fall with their constant velocity. Although when we mathematically work out the time it takes to reach this speed, it comes out infinite. So actually resistive force will always be a bit lesser than the gravitational force.
Although a complete mathematical description ( like the one given above ) proves the point to be proven. But a more intuitive and physical approach to this question can be thought of this way. The nature of all resistive forces is essentially to decrease the relative motion between the contact surfaces. So no friction force/resistive force will have the nature to make the objects speed keep on increasing forever. Although it can't prove that in a particular case with other forces also acting on the object, whether the terminal velocity will be zero or not. We have to work out all the math if we want an exact answer. 
