iPad 2 won't keep 'remember me' cookie on a website I'm running an iPad 2 on iOS7.

I have 3 iPad 2 and an iPad mini. All running iOS7. On all of the devices, I access a site which has a 'remember me' cookie to save me having to log in again. This works fine on all devices except for one iPad 2. I have gone through all the safari settings and they match the other devices. I'm stuck now. What is the problem? It happened on iOS6 as well. The cookie appears to get deleted when I turn the ipad off and then back on.

I cleared the cookies and data in case that was the problem, but it still doesn't remember on this device.
Make sure safari is not running in "private" mode.  Open Safari, tap on the multiple tabs icon (should be furthest to right), and make sure private is not highlighted.