Uhh, I actually don’t know the answer to that. Orbital mechanics is hard; see me being bamboozled elsewhere in the thread. At some point I’m guessing tidal forces from the sun would start having a major impact, since in reality they’re both in it’s gravitational well at the same time as they orbit each other. Usually that doesn’t make orbits more stable.
Also, the sun will go red giant in 4 or 5 billion years, and will eat Venus for sure. The Earth and Moon may well suffer the same fate, we’re kind of right on the projected edge.