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It sounds to me like the option to save Names and Passwords is not turned on.
Whether you’re logging in to a website, signing up for a service, or making a purchase, you can fill in a web form using the onscreen keyboard or have Safari fill it in for you using AutoFill.
- Logging in to the same site frequently? When you’re asked if you want to save the password for the site, tap Yes. The next time you visit, your user name and password will be filled in for you.
From: iPhone User Guide
You can find this in Settings > Safari >Passwords & AutoFill > Nmaes and Passwords