I believe it depends on the specifics of the merger, but my understanding is the reason black holes that orbit each other merge at all is because they bleed energy to gravitational waves. While they are at a reasonable distance, that's a very small amount of energy. I think some of these systems would be stable for billions of years.

Billions seemed too long to me, at that point you're talking about tenths of the lifetime of the universe!

That's the timescale the solar system is stable on.

Aw, sorry. I think I mis-interpreted your comment. I was thinking more of how long the system has been falling apart for. It didn't make sense to me that that could have been for billions of years, since the movement involved would be so slow?