I have an iPad 2 and it won't save the password for my google account,pinterest or any other sites I went to "settings" then Safari, then turned on "remember password" and it still doesn't work. I love my iPad but this is very annoying.
Is your autofill for names and passwords turned on? I would try clearing the saved passwords and all website data, then try again. If that doesn't work you could always download an alternative browser from the App Store.
