From Macworld: The issue that iPhone keeps asking for iCloud login and password is an old bug, but one that we keep seeing, even after the latest iOS 9 update. Sometimes an iPhone gets into a loop of continuously asking for your iCloud login details and password. Even when you enter your Apple ID, and password, it quickly asks for it again and again.
Having an iPhone that is stuck in the iCloud login loop can be extremely frustrating. Fortunately, help is at hand. In this feature we have five different fixes for the iCloud login loop.
Slide to power off
The iCloud login loop bug can be caused by a faulty Wi-Fi connection, and the easiest way to fix it is to power down the iPhone and power it back up again. This only takes a few minutes, and if it fixes the problem, it’ll save you a lot of other troubleshooting. Follow these steps to switch your iPhone off and on again:
> Hold down the Sleep/Wake button (on the top of the iPhone, or on the righthand side if it’s a ‘Plus’ model) for around five seconds until Slide To Power Off appears.
> Slide the power icon to the right.
> Wait around 30 seconds for the screen to go completely black.
> Press the Sleep/Wake button to switch the phone back on.
> When it wakes up, it’ll take a while before starting up iCloud.
You may be asked for your iCloud password, but once it’s entered one more time you should be fine.
If resetting your iPhone doesn’t fix the problem, then try signing out of iCloud and then back in again. Follow these steps:
> Open Settings > iCloud.
> Scroll down and tap Sign Out.
>Tap Sign Out.
> Tap Delete from iPhone.
> Now tap Sign In.
> Enter your Apple ID and Password.
> Resetting iCloud may fix the problem, but if that doesn’t work then, you can try to backup and restore the iPhone.
Check iCloud is working
Before going any further, we suggest that you check that iCloud is working correctly at Apple’s end. Go to https://www.apple.com/uk/support/systemstatus/ on your Mac or iPhone and check that all the services are lit up green. If there is a problem with iCloud at Apple’s end, then it’s best to give Apple a couple of hours to fix it.
Reset your password
If none of the earlier steps have worked, and you’ve checked Apple System Status, then the next thing is to change your Apple ID password. It’s a hassle, but often it fixes the problem. Changing your password is easiest on your Mac (or Windows PC).
> Open the Safari web browser and go to appleid.apple.com.
> Click ‘Reset your password’.
> Enter your Apple ID and click Next.
> Choose Email authentication or Answer Security Questions and click Next.
> Click Reset Password in the email, or enter the security questions.
> Enter a new password in the New Password and Confirm Password fields.
> Click Reset Password.
Now try entering the new password on your iPhone when it asks. This should be accepted by the iPhone and fix the problem.
Backup and Restore
If your iPhone is constantly asking for the iCloud password, and you’ve tried power cycling the iPhone and changing your password, then the last step is to back up and restore your iPhone.
You’ll need to back up your iPhone to a Mac because you won’t be able to rely on iCloud Backup.
> Connect your iPhone to the Mac using the USB Cable.
> Open iTunes.
> Click Devices and choose your iPhone.
> Select Summary.
> Choose This Computer under Backups.
> Click Back Up Now.
Wait for the backup process to take place (you’ll see a blue progress bar at the top of iTunes). When it’s finished you can begin the process of restoring your iPhone:
> Keep your iPhone connected to the Mac.
> On your iPhone click Settings > iCloud.
> Tap Find My iPhone.
>Set Find My iPhone to Off.
> Enter your Apple ID Password and tap Turn Off.
> Back in iTunes on your Mac, click Restore iPhone.
Follow the restore process and use the Backup you just created when going through the restore process. You will download the latest version of iOS from Apple, and restore your iPhone using the backup. It will be in the same condition as before, but this will hopefully have fixed the problem.