Cookies and passwords not stored

I frequently visit the BBC and Guardian websites from my iPad Mini. I am registered with both sites, have signed in and selected the "keep me signed in" option. However, I often find when visiting the sites that they treat me as a new user, asking me to accept cookies afresh. There doesn't seem to be any pattern behind when this occurs so I almost as to the cause. I've set my iPad to accept cookies and to allow me to store passwords and form information. It's getting annoying having to sign into the same websites several times. Does anyone know how I might rectify this situation?