Hello ED. The
F and
a in
F=ma are actually vectors - meaning they have both
magnitude and
direction - and the equation should properly be written as

, meaning that you have to add up all the forces acting on the object to find the total magnitide and direction of

. So
F=ma leads to a result of constant acceleration ONLY if the sum of the forces acting on the object is constant.
In the example of the falling object, the force of gravity acting on it in the downward direction is resisted by a force of air resistance acting on it in the upward direction. The magnitiude of the air resistance increases as the object's velocity increases. At first air resistance is nil, and the object falls with an aceleration that is

, or

. But as the velocity increases you need to consider the upward force of air resistance:
As long as

is less than the object's weight, it continues to accelerate as it falls, although at a smaller rate than before. At some point the magnitude of the air resistance equals the magnitude of the object's weight, so that

, and the object no longer continues to accelerate. At that point it has reached its "terminal veocity."
Hope this explanation helps.