iphone 4s running ios 7 keeps asking to sign into icloud after update

Wife updated her 8 gig iphone 4s to IOS 7.1.2. As soon as the smoke cleared everything seemed fine until the phone started asking her to input her apple ID and password. The first few times she entered it thinking it was normal. After a few days of doing this 2-3 times a day she just hits cancel. I did a bit of research and found that it might have something to do with the limited memory on the 4s and the lack of forsight on Apple's part when developing gargantuan operating systems. Any fixes out there besides buying a new phone?