I can't get tapcon screws to tap into the concrete slab!?

My husband and I are installing a 5/8" plywood subfloor plus 1" foam over our concrete slab. We are using 3/16 tapcon screws that are 2 3/4" long. We have rented a hammer drill, and are using a 5/32 bit to drill into the concrete. We are drilling down 1/4" longer than the screw, but the screws don't seem to be tapping into the concrete. Maybe our regular drill does not have enough power to get the screws to go down?? Do we need a drill with more torque to get the screws to go in?? Does anyone know why we might be having trouble? What can I do to fix this?