Why does iCloud continue to ask for my password after inputting it correctly?

I've seen threads addressing this issue elsewhere but I'm not sure how to get back. I'm sick and tired of several issues related to iCloud going bonkers. I'm using iOS 7 on my 4S and iPad 4, only having issues on the phone. Multiple times now iCloud has just randomly TURNED OFF find my iphone, and other features (contacts, calendars, etc) so that on one occasion I had lost ALL my contacts, only to have them restored when I turned iCloud back on. Now iCloud seems to be on the fritz, turning on and off and CONSTANTLY RE-PROMPTING me for my password AFTER inputting it correctly. It's infuriating and annoying and I wish there was a solution. KILL THESE BUGS APPLE.

Just FYI, I've tried re-starting my phone, re-entering my password all to no avail. As far as I can tell, this is a buggy software issue.

Thanks for any help you can offer.