Relativity and the orbits of Alpha Centauri

The most pronounced effect that gravity traveling at the velocity of light has on an orbital structure happens to be in binary pairs because both objects have significant velocity. There is a gap between the object’s position and the gravity-origin because of that higher velocity. The further gravity has to travel, the wider this gap becomes as a gravity-delay.

Scenario [2] of the algorithm orbit-gravity-sim-12.exe applies gravity traveling at the velocity of light to the Alpha Centauri system:
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Not only will the Alpha Centauri pair move apart at more than 1.4 million km per orbit because of gravity traveling at the velocity of light, but the amount of change is itself increasing by hundreds of km each orbit. The outer distance increases much faster than the inner distance, thus the pair becomes more eccentric with each orbit.

The outwards spiral of 1.4mkm per orbit is big enough to be visible on the scale of the computer-screen, which is here depicted as being 1 pixel = 15mkm. So they move apart by 1 pixel about every 11 orbits:
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When compared to the previous diagram, the orbit-lines have both visibly become thicker at the outer limits after 50 orbits as they move away from one another. But it is most apparent when watching it generate in real-time.

So how long will it take before they fall apart completely? What would the life-span be of the Alpha Centauri binary under the Relativistic notion of gravity traveling at the velocity of light?