Log in for website does not remember me
There is a website I frequent that requires a login. It also has a "remember me" button. But it doesn't remember me. This is on my iPhone 5S with 8.0.2 update.
That function on a website typically needs cookies. Settings app > Safari > Block Cookies. This should set to Allow from Websites I visit (or minimally Allow from Current Website Only). Also, check Passwords&Autofill to see that Names ans passwords are On.