I posted on this topic before because I also suffered from iCloud password prompting, iCloud random feature turn off's and sluggish performance. This was on an IPhone 4S.
I reported this to apple and went through the process of restore to New, and tried to repeat the problem (by running memory extension games like HayDay and Clash of Clans). I could not repeat the issue after a restore to New with just a few apps loaded. Apple then cancelled my support ticket.
Of course I wanted all my app's and data back, so I restored from Backup and the issue returned. I avoided the issue as much as I could by closing down all apps when not in use and regular reboot's of the phone - it was annoying and I still occasionally had the 'Find my IPhone' feature turn off, and sometimes iCloud would lose the plot.
I then upgraded my handset to an IPhone 5S. Everything went great for 2 months, and then I got the issue again!
I was really beating up the IPhone 5s though - was playing Clash of Clans, Hay Day and Boom Beach - all memory intensive and all at the same time. It took about 3 weeks of playing these games with no reboot of the phone and I noticed that display rendering was lagging and then I got prompted for my iCloud password and my 'Find my IPhone' iCloud option was turned OFF! I did a reboot of the phone and it's been fine - but I'm guessing it'll happen again in a couple of weeks.
iOS 7 defnitely has a memory leak - and as your running memory RAM fills up you may get unlucky and it'll override some system memory - more than likely in the iCloud area of code. I've basically now proven that it's the Operating System (and I'm on 7.1) and it can takes weeks for the issue to surface on a brand new IPhone 5S.
I really hope the Apple developers read this thread and look more closely into checking for memory leaks and finally fix this issue!
Hope this helps.