'96 Honda Civic AC Flow weakens as air gets colder?

I'm driving a 1996 Honda Civic EX, and my AC is acting up. When I first start the car, the airflow is normal even though it hasn't cooled yet, but after the air gets cool enough, the flow weakens. In other words, I could be running my AC on high and it'll feel like it's running on low once the air has gotten cool enough. Any thoughts on what the problem could be and how much it would cost to fix it?