Thanks griff w but unfortunately found nothing of help there.
"keeps asking me to approve security code and when I write it, it asks me again. And keeps repeating. I chose approve from other device (I have a MBA) but nothing appeared on it. The Keychain button in iOS setting says pending."
Exactly the same here.
The AppleSupport article is useless it skims by saying, "follow instructions on screen"
Essentially if you are stuck in this pending loop. You're stuck !
What you'll probably have to do is reset your keychain. you can do that by going to (on your Mac) System Preferences > iCloud > select Keychain (and enter your password) > Use Code... > Forgot Code? > Reset Keychain...
Then you can go ahead and recreate your keychain from any device of your choosing (Mac, iPhone, iPad).
The device you choose will have it's keychain data uploaded to iCloud and be the master keychain that the rest of your devices will then merge with.
-hope that helps
I too am having the same issue and it started with iOS 8 on my iPhone 5s. Keychain will not turn "OFF" but will stay "Pending". Then about once a week I find a message on the phone saying I have to authorize Keychain. It doesn't matter if I type the code or authorize with another device it always fails.
My iPad 2 running iOS 8 works great! Keychain is turned off and stays that way.
I have exclusively used iPhone since the beginning in 2007, but I have to be honest, I think this was the last straw for me and Apple iPhone as I don't think I'll get another one. The bigger Apple gets the worse their 'Services' get. iCloud crashes left and right, Photostream doesn't work half the time. Every new iOS update adds a folder where photos are stored on the phone making it ultra confusing where the last picture I took is. Then iTunes stops Wifi syncing with the phone so I have to power it down and back up to get iTunes to see it again. It's just too much Apple! I need a phone that 'Just Works' as advertised, not one that I have to tweak/shut off/reset all the time to get to work.