I have noticed that when I bribe Independent Peoples (probably also for praising) the positive change in influence per turn eventually goes back to 0.

Is that intended? What determines when and how that happens?

Noticed that in my current game. I noticed when I killed units of an aggressive Independent People, influence went down. It's possible it's also affected by how strongly they're being affected by your culture. Your sphere of influence appears to contribute, so if they're well outside, any bribe you give will eventually decay.

Thanks for the info.
I have since found that my donations seem to last for precisely 11 turns (on Endless speed). The influence count always halts at 22, 44, 66, 88.