If you’re facing a continuous problem with iCloud asking your login details all the time then it possible to fix this problem by various ways which are given below.
Actually this is simple problem where new has appeared in iOS 8 and has even carried over into iOS 9. The culprit is a faulty Wi-Fi connection. It’ll be hard to get to the settings options to fix your Wi-Fi connection with the iCloud pop-up asking you to login every minute. However, there are a few ways to get out of this issue.
Reconnect to your Wi-Fi
From your Phone tap Settings > Wi-Fi. Make sure your Wi-Fi is turned on. Next, tap your Wi-Fi network name and enter the password if needed.
If iCloud interrupts you from reconnecting your Wi-Fi, a Hard Reset may do the trick. A Hard Reset is when you hold down the home button and power button at the same time until the screen goes blank. From here press the power button and turn your phone back on. Head over to setting > Wi-Fi and join a network. It’ll take a while before iCloud starts up again, so you should have enough time to fix your connection before it pops up again.
If the reset doesn’t work. Try signing out of iCloud. You can do this by going to Settings > iCloud. Then, scroll down and tap sign out. Next, tap Delete from iPhone and re-sign in by entering your Apple ID and password.
If none of the above works, your next best bet is to restore your iPhone. First, back up your iPhone by connecting to a Mac using a USB Cable. Then open iTunes and click Devices, choose your iPhone and select summary. Next click choose this computer under Backups and click Backup Now. Once the Backup process has taken place you can begin restoring your iPhone.
To restore your iPhone, keep it connected to the Mac. From the phone click on Settings > iCloud. Next, tap Find my phone and Set it to Off. Enter your Apple ID password and tap turn off. From your Mac in iTunes, Click restore iPhone. After following the Restore process on the screen, this should fix the iCloud problem.
If you want to know the more information about trouble shooting the iCloud account then simply visit Apple support page.