ICloud sign in keeps popping up in my iPhone 4s on a loop. Is there any way I can stop this?

Question

I've tried to type in my password and such, but it never stops popping up. Any help?

Answer 1

I was very annoyed before, but have resolved this issue without resorting to violence. In the interests of posterity, I'll post what I did here.
Basically, I got ready to wipe the device. I moved all the photos and videos off the device (iPod Touch 5) and downloaded the latest iTunes to a PC here. Then I connected the device to the iTunes PC (which had previously been used with the device.)
At this point, it was still asking me to log on on the iPod, and no Wi-Fi connection.
I then initiated a backup from iTunes to make sure we had all the installed apps and music etc. As the backup started, I clicked "cancel" on the login prompt, and lo and behold, the backup process stalled the iCloud thing for long enough for a Wi-Fi connection to be established. A few seconds later, the iCloud prompt came up again, and I was able to successfully log on.
After that, I deleted the iCloud account, and now everything is working fine.
Looks like I needed to get the device thinking about somethign else for long enough for the Wi-Fi to hook up.
Won't work for everyone, but worth a try, as it meant no resetting, no trips to the "genius" bar, and no stuffing around with restores.
Thanks for the ideas everyone, and happy to contribute my 2c back to the crowd.
Hope this is the last time I have anything to do with my daughter's iPod (or any other Apple support!)
And thanks to Host for censoring my Apple h8 above. I'm stil feeling the burn, but the flames are low at present.