Possible.
Modify the circuit so that pressing that button (such as if it's looking for a logical high pulse etc... ) sends the logical high pulse for only 1 frame and then opens the circuit again regardless of button position and won't send out a signal again until button is unpressed.
Controllers aren't generally too complicated when it comes to the buttons themselves. This could be accomplished using a flip-flop that "sets" only on the positive transient of the signal that comes in, thus when pressed and going from low to high, it "sets" and sends the signal out, then has a loopback from that output of the flip-flop which feeds a timeslicer which after 1/60 of a second sends a signal to "clear" the state of the flip-flop. Then it won't "set" again until you stop pressing the button, where the signal to the flip-flop goes low again, and then the button is once again pressed.
It will then automatically "unpress" the button after 1 frame (1/60th of a second) even if the button is still held down but wouldn't "press" until you released the button and then pressed it again. Basically, you could do it with relatively few components provided you cracked open the controller, looked at the circuitry, determined what the signal looks like and how it works within the circuit, and then worked a few components into the mix.
