While the recession of our Moon from the Earth may slow and even stop,
binary star systems will
(1) never stop experiencing mutual tidal forces, (2) continuously experience loss of mass and gravitational attraction, (3) lose energy by gravitational wave radiation.
Assuming all these three mechanisms are extant, can binary stars break away from each other?
The one comment so far notes that LIGO measures effects of the convergence of gravitational bodies, that larger orbits have more energy, and dissipation of energy will reduce the orbital distances. I would appreciate an appropriate reference.
The moon is retreating from the Earth which is said to be mostly due to tidal-related dissipation. This phenomenon seems opposite the commentor's view.
A mechanism relating to binary stars, especially those that whose orbits bring them close together, is a possible exchange of mass. An expert might tell us how this exchange might affect orbits. If indeed the stars are close, then we might expect a decay in orbit due to simple drag.
I assume "expansion of the universe" is not a factor in these scales of distance and time. Thanks to all for your time on this question.