I think 10 turns
I think that's speed specific. I play marathon and they last longer but every turn there is less unhealthy points. So it dissipates slowly until it's all gone.
Well, when you go to poison an A.I.'s water it says it will last for 10 turns (and I play marathon, so I'm guessing it would be shorter for faster speeds), so I assume its the same when they do it to you.