I had a number of enemy planets showing the little red "in danger of flipping" icon and figured I would just let them flip instead of invading them - my brilliant AI enemy had sent colony ships into my territory to claim "extreme" worlds and I let them through.
One planet flipped to me, but the game crashed.
I reloaded, and the planet did not flip - I figure there is randomness, so no biggie. I noticed the red icon was no longer there though.
I only had short periods of time to play in this time though, so I'd play just a couple turns at a time...and I noticed none of these planets *deep* within my territory were flipping (and I was destroying any ships they built to garrison).
This leads me to wonder if culture flipping gets reset by saving and loading?